diff --git a/pandas/_libs/algos.pxd b/pandas/_libs/algos.pxd
index 5df1e381ea3ce..4bca5b33a3c62 100644
--- a/pandas/_libs/algos.pxd
+++ b/pandas/_libs/algos.pxd
@@ -1,4 +1,4 @@
-from util cimport numeric
+from pandas._libs.util cimport numeric
 
 
 cdef inline Py_ssize_t swap(numeric *a, numeric *b) nogil:
diff --git a/pandas/_libs/algos.pyx b/pandas/_libs/algos.pyx
index e77899507833f..a064aec492df2 100644
--- a/pandas/_libs/algos.pyx
+++ b/pandas/_libs/algos.pyx
@@ -19,15 +19,14 @@ from numpy cimport (ndarray,
 cnp.import_array()
 
 
-cimport util
-from util cimport numeric, get_nat
+cimport pandas._libs.util as util
+from pandas._libs.util cimport numeric, get_nat
 
-from khash cimport (khiter_t,
-                    kh_destroy_int64, kh_put_int64,
-                    kh_init_int64, kh_int64_t,
-                    kh_resize_int64, kh_get_int64)
+from pandas._libs.khash cimport (
+    khiter_t, kh_destroy_int64, kh_put_int64, kh_init_int64, kh_int64_t,
+    kh_resize_int64, kh_get_int64)
 
-import missing
+import pandas._libs.missing as missing
 
 cdef float64_t FP_ERR = 1e-13
 
diff --git a/pandas/_libs/groupby.pyx b/pandas/_libs/groupby.pyx
index 7c16b29f3e42b..e6036654c71c3 100644
--- a/pandas/_libs/groupby.pyx
+++ b/pandas/_libs/groupby.pyx
@@ -13,11 +13,13 @@ from numpy cimport (ndarray,
 cnp.import_array()
 
 
-from util cimport numeric, get_nat
+from pandas._libs.util cimport numeric, get_nat
 
-from algos cimport (swap, TiebreakEnumType, TIEBREAK_AVERAGE, TIEBREAK_MIN,
-                    TIEBREAK_MAX, TIEBREAK_FIRST, TIEBREAK_DENSE)
-from algos import take_2d_axis1_float64_float64, groupsort_indexer, tiebreakers
+from pandas._libs.algos cimport (swap, TiebreakEnumType, TIEBREAK_AVERAGE,
+                                 TIEBREAK_MIN, TIEBREAK_MAX, TIEBREAK_FIRST,
+                                 TIEBREAK_DENSE)
+from pandas._libs.algos import (take_2d_axis1_float64_float64,
+                                groupsort_indexer, tiebreakers)
 
 cdef int64_t NPY_NAT = get_nat()
 
diff --git a/pandas/_libs/hashing.pyx b/pandas/_libs/hashing.pyx
index 6e66693decc01..21d6c5378e170 100644
--- a/pandas/_libs/hashing.pyx
+++ b/pandas/_libs/hashing.pyx
@@ -9,7 +9,7 @@ import numpy as np
 from numpy cimport uint8_t, uint32_t, uint64_t, import_array
 import_array()
 
-from util cimport is_nan
+from pandas._libs.util cimport is_nan
 
 DEF cROUNDS = 2
 DEF dROUNDS = 4
diff --git a/pandas/_libs/hashtable.pxd b/pandas/_libs/hashtable.pxd
index d735b3c0673b2..609420f429798 100644
--- a/pandas/_libs/hashtable.pxd
+++ b/pandas/_libs/hashtable.pxd
@@ -1,5 +1,6 @@
-from khash cimport (kh_int64_t, kh_uint64_t, kh_float64_t, kh_pymap_t,
-                    kh_str_t, uint64_t, int64_t, float64_t)
+from pandas._libs.khash cimport (
+    kh_int64_t, kh_uint64_t, kh_float64_t, kh_pymap_t, kh_str_t, uint64_t,
+    int64_t, float64_t)
 from numpy cimport ndarray
 
 # prototypes for sharing
diff --git a/pandas/_libs/hashtable.pyx b/pandas/_libs/hashtable.pyx
index 9aa887727a765..47fa5932290af 100644
--- a/pandas/_libs/hashtable.pyx
+++ b/pandas/_libs/hashtable.pyx
@@ -16,7 +16,7 @@ cdef extern from "numpy/npy_math.h":
     float64_t NAN "NPY_NAN"
 
 
-from khash cimport (
+from pandas._libs.khash cimport (
     khiter_t,
 
     kh_str_t, kh_init_str, kh_put_str, kh_exist_str,
@@ -37,9 +37,9 @@ from khash cimport (
     kh_put_pymap, kh_resize_pymap)
 
 
-cimport util
+cimport pandas._libs.util as util
 
-from missing cimport checknull
+from pandas._libs.missing cimport checknull
 
 
 cdef int64_t NPY_NAT = util.get_nat()
diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index d828c3dd8e923..365713d579d60 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -15,11 +15,11 @@ from numpy cimport (ndarray, intp_t,
 cnp.import_array()
 
 
-cimport util
+cimport pandas._libs.util as util
 
-from tslibs.conversion cimport maybe_datetimelike_to_i8
+from pandas._libs.tslibs.conversion cimport maybe_datetimelike_to_i8
 
-from hashtable cimport HashTable
+from pandas._libs.hashtable cimport HashTable
 
 from pandas._libs import algos, hashtable as _hash
 from pandas._libs.tslibs import Timestamp, Timedelta, period as periodlib
diff --git a/pandas/_libs/internals.pyx b/pandas/_libs/internals.pyx
index e0f26357cae6f..72a1cf16f96b6 100644
--- a/pandas/_libs/internals.pyx
+++ b/pandas/_libs/internals.pyx
@@ -18,7 +18,7 @@ cdef extern from "compat_helper.h":
                                Py_ssize_t *slicelength) except -1
 
 
-from algos import ensure_int64
+from pandas._libs.algos import ensure_int64
 
 
 cdef class BlockPlacement:
diff --git a/pandas/_libs/interval.pyx b/pandas/_libs/interval.pyx
index 1484a1299b246..3a522baaa92af 100644
--- a/pandas/_libs/interval.pyx
+++ b/pandas/_libs/interval.pyx
@@ -17,13 +17,13 @@ from numpy cimport (
 cnp.import_array()
 
 
-cimport util
+cimport pandas._libs.util as util
 util.import_array()
 
-from hashtable cimport Int64Vector, Int64VectorData
+from pandas._libs.hashtable cimport Int64Vector, Int64VectorData
 
-from tslibs import Timestamp
-from tslibs.timezones cimport tz_compare
+from pandas._libs.tslibs import Timestamp
+from pandas._libs.tslibs.timezones cimport tz_compare
 
 
 _VALID_CLOSED = frozenset(['left', 'right', 'both', 'neither'])
diff --git a/pandas/_libs/join.pyx b/pandas/_libs/join.pyx
index 54dfeeff1452d..e4440ac3d9fd8 100644
--- a/pandas/_libs/join.pyx
+++ b/pandas/_libs/join.pyx
@@ -656,7 +656,7 @@ outer_join_indexer_uint64 = outer_join_indexer["uint64_t"]
 # asof_join_by
 # ----------------------------------------------------------------------
 
-from hashtable cimport (
+from pandas._libs.hashtable cimport (
     HashTable, PyObjectHashTable, UInt64HashTable, Int64HashTable)
 
 ctypedef fused asof_t:
diff --git a/pandas/_libs/lib.pyx b/pandas/_libs/lib.pyx
index 3bc39979b0fc1..d6e2b9a5288f5 100644
--- a/pandas/_libs/lib.pyx
+++ b/pandas/_libs/lib.pyx
@@ -49,18 +49,19 @@ cdef extern from "numpy/arrayobject.h":
 cdef extern from "src/parse_helper.h":
     int floatify(object, float64_t *result, int *maybe_int) except -1
 
-cimport util
-from util cimport is_nan, UINT64_MAX, INT64_MAX, INT64_MIN
-
-from tslib import array_to_datetime
-from tslibs.nattype cimport NPY_NAT
-from tslibs.nattype import NaT
-from tslibs.conversion cimport convert_to_tsobject
-from tslibs.timedeltas cimport convert_to_timedelta64
-from tslibs.timezones cimport get_timezone, tz_compare
-
-from missing cimport (checknull, isnaobj,
-                      is_null_datetime64, is_null_timedelta64, is_null_period)
+cimport pandas._libs.util as util
+from pandas._libs.util cimport is_nan, UINT64_MAX, INT64_MAX, INT64_MIN
+
+from pandas._libs.tslib import array_to_datetime
+from pandas._libs.tslibs.nattype cimport NPY_NAT
+from pandas._libs.tslibs.nattype import NaT
+from pandas._libs.tslibs.conversion cimport convert_to_tsobject
+from pandas._libs.tslibs.timedeltas cimport convert_to_timedelta64
+from pandas._libs.tslibs.timezones cimport get_timezone, tz_compare
+
+from pandas._libs.missing cimport (
+    checknull, isnaobj, is_null_datetime64, is_null_timedelta64, is_null_period
+)
 
 
 # constants that will be compared to potentially arbitrarily large
diff --git a/pandas/_libs/missing.pyx b/pandas/_libs/missing.pyx
index 1fdb04dd10d8e..c7f06bc5d7d4f 100644
--- a/pandas/_libs/missing.pyx
+++ b/pandas/_libs/missing.pyx
@@ -8,11 +8,12 @@ cimport numpy as cnp
 from numpy cimport ndarray, int64_t, uint8_t, float64_t
 cnp.import_array()
 
-cimport util
+cimport pandas._libs.util as util
 
-from tslibs.np_datetime cimport get_timedelta64_value, get_datetime64_value
-from tslibs.nattype cimport checknull_with_nat
-from tslibs.nattype import NaT
+from pandas._libs.tslibs.np_datetime cimport (
+    get_timedelta64_value, get_datetime64_value)
+from pandas._libs.tslibs.nattype cimport checknull_with_nat
+from pandas._libs.tslibs.nattype import NaT
 
 cdef float64_t INF = <float64_t>np.inf
 cdef float64_t NEGINF = -INF
diff --git a/pandas/_libs/ops.pyx b/pandas/_libs/ops.pyx
index e21bce177b38b..fb1d2e379958c 100644
--- a/pandas/_libs/ops.pyx
+++ b/pandas/_libs/ops.pyx
@@ -12,9 +12,9 @@ from numpy cimport ndarray, uint8_t, import_array
 import_array()
 
 
-from util cimport UINT8_MAX, is_nan
+from pandas._libs.util cimport UINT8_MAX, is_nan
 
-from missing cimport checknull
+from pandas._libs.missing cimport checknull
 
 
 @cython.wraparound(False)
diff --git a/pandas/_libs/parsers.pyx b/pandas/_libs/parsers.pyx
index a459057555cf3..169aa4ffe72da 100644
--- a/pandas/_libs/parsers.pyx
+++ b/pandas/_libs/parsers.pyx
@@ -32,10 +32,10 @@ cimport numpy as cnp
 from numpy cimport ndarray, uint8_t, uint64_t, int64_t, float64_t
 cnp.import_array()
 
-from util cimport UINT64_MAX, INT64_MAX, INT64_MIN
-import lib
+from pandas._libs.util cimport UINT64_MAX, INT64_MAX, INT64_MIN
+import pandas._libs.lib as lib
 
-from khash cimport (
+from pandas._libs.khash cimport (
     khiter_t,
     kh_str_t, kh_init_str, kh_put_str, kh_exist_str,
     kh_get_str, kh_destroy_str,
diff --git a/pandas/_libs/reduction.pyx b/pandas/_libs/reduction.pyx
index a61295f781901..ca39c4de4d309 100644
--- a/pandas/_libs/reduction.pyx
+++ b/pandas/_libs/reduction.pyx
@@ -15,8 +15,8 @@ from numpy cimport (ndarray,
                     flatiter)
 cnp.import_array()
 
-cimport util
-from lib import maybe_convert_objects
+cimport pandas._libs.util as util
+from pandas._libs.lib import maybe_convert_objects
 
 
 cdef _get_result_array(object obj, Py_ssize_t size, Py_ssize_t cnt):
diff --git a/pandas/_libs/tslib.pyx b/pandas/_libs/tslib.pyx
index 3f2b49d141e18..798e338d5581b 100644
--- a/pandas/_libs/tslib.pyx
+++ b/pandas/_libs/tslib.pyx
@@ -16,36 +16,33 @@ cnp.import_array()
 
 import pytz
 
-from util cimport (is_integer_object, is_float_object, is_string_object,
-                   is_datetime64_object)
+from pandas._libs.util cimport (
+    is_integer_object, is_float_object, is_string_object, is_datetime64_object)
 
 
-from tslibs.np_datetime cimport (check_dts_bounds,
-                                 npy_datetimestruct,
-                                 _string_to_dts,
-                                 dt64_to_dtstruct, dtstruct_to_dt64,
-                                 pydatetime_to_dt64, pydate_to_dt64,
-                                 get_datetime64_value)
-from tslibs.np_datetime import OutOfBoundsDatetime
+from pandas._libs.tslibs.np_datetime cimport (
+    check_dts_bounds, npy_datetimestruct, _string_to_dts, dt64_to_dtstruct,
+    dtstruct_to_dt64, pydatetime_to_dt64, pydate_to_dt64, get_datetime64_value)
+from pandas._libs.tslibs.np_datetime import OutOfBoundsDatetime
 
-from tslibs.parsing import parse_datetime_string
+from pandas._libs.tslibs.parsing import parse_datetime_string
 
-from tslibs.timedeltas cimport cast_from_unit
-from tslibs.timezones cimport is_utc, is_tzlocal, get_dst_info
-from tslibs.timezones import UTC
-from tslibs.conversion cimport (tz_convert_single, _TSObject,
-                                convert_datetime_to_tsobject,
-                                get_datetime64_nanos,
-                                tz_convert_utc_to_tzlocal)
+from pandas._libs.tslibs.timedeltas cimport cast_from_unit
+from pandas._libs.tslibs.timezones cimport is_utc, is_tzlocal, get_dst_info
+from pandas._libs.tslibs.timezones import UTC
+from pandas._libs.tslibs.conversion cimport (
+    tz_convert_single, _TSObject, convert_datetime_to_tsobject,
+    get_datetime64_nanos, tz_convert_utc_to_tzlocal)
 
 # many modules still look for NaT and iNaT here despite them not being needed
-from tslibs.nattype import nat_strings, iNaT  # noqa:F821
-from tslibs.nattype cimport checknull_with_nat, NPY_NAT, c_NaT as NaT
+from pandas._libs.tslibs.nattype import nat_strings, iNaT  # noqa:F821
+from pandas._libs.tslibs.nattype cimport (
+    checknull_with_nat, NPY_NAT, c_NaT as NaT)
 
-from tslibs.offsets cimport to_offset
+from pandas._libs.tslibs.offsets cimport to_offset
 
-from tslibs.timestamps cimport create_timestamp_from_ts
-from tslibs.timestamps import Timestamp
+from pandas._libs.tslibs.timestamps cimport create_timestamp_from_ts
+from pandas._libs.tslibs.timestamps import Timestamp
 
 
 cdef bint PY2 = str == bytes
diff --git a/pandas/_libs/tslibs/ccalendar.pyx b/pandas/_libs/tslibs/ccalendar.pyx
index 91e7d83012bad..c48812acd3de1 100644
--- a/pandas/_libs/tslibs/ccalendar.pyx
+++ b/pandas/_libs/tslibs/ccalendar.pyx
@@ -9,7 +9,7 @@ import cython
 from numpy cimport int64_t, int32_t
 
 from locale import LC_TIME
-from strptime import LocaleTime
+from pandas._libs.tslibs.strptime import LocaleTime
 
 # ----------------------------------------------------------------------
 # Constants
diff --git a/pandas/_libs/tslibs/conversion.pxd b/pandas/_libs/tslibs/conversion.pxd
index 4eb93c35b4afc..8aca9ca185243 100644
--- a/pandas/_libs/tslibs/conversion.pxd
+++ b/pandas/_libs/tslibs/conversion.pxd
@@ -4,7 +4,7 @@ from cpython.datetime cimport datetime, tzinfo
 
 from numpy cimport int64_t, int32_t
 
-from np_datetime cimport npy_datetimestruct
+from pandas._libs.tslibs.np_datetime cimport npy_datetimestruct
 
 
 cdef class _TSObject:
diff --git a/pandas/_libs/tslibs/conversion.pyx b/pandas/_libs/tslibs/conversion.pyx
index 81f2aeae68136..6e4d79d7b6f9e 100644
--- a/pandas/_libs/tslibs/conversion.pyx
+++ b/pandas/_libs/tslibs/conversion.pyx
@@ -16,30 +16,28 @@ from cpython.datetime cimport (datetime, tzinfo,
                                PyDateTime_CheckExact, PyDateTime_IMPORT)
 PyDateTime_IMPORT
 
-from ccalendar import DAY_SECONDS, HOUR_SECONDS
-
-from np_datetime cimport (check_dts_bounds,
-                          npy_datetimestruct,
-                          pandas_datetime_to_datetimestruct, _string_to_dts,
-                          npy_datetime,
-                          dt64_to_dtstruct, dtstruct_to_dt64,
-                          get_datetime64_unit, get_datetime64_value,
-                          pydatetime_to_dt64, NPY_DATETIMEUNIT, NPY_FR_ns)
-from np_datetime import OutOfBoundsDatetime
-
-from util cimport (is_string_object,
-                   is_datetime64_object,
-                   is_integer_object, is_float_object)
-
-from timedeltas cimport cast_from_unit
-from timezones cimport (is_utc, is_tzlocal, is_fixed_offset,
-                        get_utcoffset, get_dst_info,
-                        get_timezone, maybe_get_tz, tz_compare)
-from timezones import UTC
-from parsing import parse_datetime_string
-
-from nattype import nat_strings
-from nattype cimport NPY_NAT, checknull_with_nat, c_NaT as NaT
+from pandas._libs.tslibs.ccalendar import DAY_SECONDS, HOUR_SECONDS
+
+from pandas._libs.tslibs.np_datetime cimport (
+    check_dts_bounds, npy_datetimestruct, pandas_datetime_to_datetimestruct,
+    _string_to_dts, npy_datetime, dt64_to_dtstruct, dtstruct_to_dt64,
+    get_datetime64_unit, get_datetime64_value, pydatetime_to_dt64,
+    NPY_DATETIMEUNIT, NPY_FR_ns)
+from pandas._libs.tslibs.np_datetime import OutOfBoundsDatetime
+
+from pandas._libs.tslibs.util cimport (
+    is_string_object, is_datetime64_object, is_integer_object, is_float_object)
+
+from pandas._libs.tslibs.timedeltas cimport cast_from_unit
+from pandas._libs.tslibs.timezones cimport (
+    is_utc, is_tzlocal, is_fixed_offset, get_utcoffset, get_dst_info,
+    get_timezone, maybe_get_tz, tz_compare)
+from pandas._libs.tslibs.timezones import UTC
+from pandas._libs.tslibs.parsing import parse_datetime_string
+
+from pandas._libs.tslibs.nattype import nat_strings
+from pandas._libs.tslibs.nattype cimport (
+    NPY_NAT, checknull_with_nat, c_NaT as NaT)
 
 # ----------------------------------------------------------------------
 # Constants
@@ -1090,7 +1088,7 @@ cdef inline Py_ssize_t bisect_right_i8(int64_t *data,
 
 cdef inline str _render_tstamp(int64_t val):
     """ Helper function to render exception messages"""
-    from timestamps import Timestamp
+    from pandas._libs.tslibs.timestamps import Timestamp
     return str(Timestamp(val))
 
 
diff --git a/pandas/_libs/tslibs/fields.pyx b/pandas/_libs/tslibs/fields.pyx
index df2a189097b78..5cda7992369fc 100644
--- a/pandas/_libs/tslibs/fields.pyx
+++ b/pandas/_libs/tslibs/fields.pyx
@@ -12,12 +12,15 @@ cimport numpy as cnp
 from numpy cimport ndarray, int64_t, int32_t, int8_t
 cnp.import_array()
 
-from ccalendar import get_locale_names, MONTHS_FULL, DAYS_FULL, DAY_SECONDS
-from ccalendar cimport (get_days_in_month, is_leapyear, dayofweek,
-                        get_week_of_year, get_day_of_year)
-from np_datetime cimport (npy_datetimestruct, pandas_timedeltastruct,
-                          dt64_to_dtstruct, td64_to_tdstruct)
-from nattype cimport NPY_NAT
+from pandas._libs.tslibs.ccalendar import (
+    get_locale_names, MONTHS_FULL, DAYS_FULL, DAY_SECONDS)
+from pandas._libs.tslibs.ccalendar cimport (
+    get_days_in_month, is_leapyear, dayofweek, get_week_of_year,
+    get_day_of_year)
+from pandas._libs.tslibs.np_datetime cimport (
+    npy_datetimestruct, pandas_timedeltastruct, dt64_to_dtstruct,
+    td64_to_tdstruct)
+from pandas._libs.tslibs.nattype cimport NPY_NAT
 
 
 def get_time_micros(ndarray[int64_t] dtindex):
diff --git a/pandas/_libs/tslibs/frequencies.pyx b/pandas/_libs/tslibs/frequencies.pyx
index fff4d04399481..bd9e68e134407 100644
--- a/pandas/_libs/tslibs/frequencies.pyx
+++ b/pandas/_libs/tslibs/frequencies.pyx
@@ -4,9 +4,9 @@ import re
 cimport numpy as cnp
 cnp.import_array()
 
-from util cimport is_integer_object, is_string_object
+from pandas._libs.tslibs.util cimport is_integer_object, is_string_object
 
-from ccalendar import MONTH_NUMBERS
+from pandas._libs.tslibs.ccalendar import MONTH_NUMBERS
 
 # ----------------------------------------------------------------------
 # Constants
diff --git a/pandas/_libs/tslibs/nattype.pyx b/pandas/_libs/tslibs/nattype.pyx
index d61b3aa3135d1..cc06e9857a44f 100644
--- a/pandas/_libs/tslibs/nattype.pyx
+++ b/pandas/_libs/tslibs/nattype.pyx
@@ -14,10 +14,10 @@ cimport numpy as cnp
 from numpy cimport int64_t
 cnp.import_array()
 
-cimport util
-from util cimport (get_nat,
-                   is_integer_object, is_float_object,
-                   is_datetime64_object, is_timedelta64_object)
+cimport pandas._libs.tslibs.util as util
+from pandas._libs.tslibs.util cimport (
+    get_nat, is_integer_object, is_float_object, is_datetime64_object,
+    is_timedelta64_object)
 
 # ----------------------------------------------------------------------
 # Constants
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index 0720f5094fa51..11ce539d25767 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -17,15 +17,16 @@ from numpy cimport int64_t
 cnp.import_array()
 
 
-from util cimport is_string_object, is_integer_object
-
-from ccalendar import MONTHS, DAYS
-from ccalendar cimport get_days_in_month, dayofweek
-from conversion cimport tz_convert_single, pydt_to_i8, localize_pydatetime
-from nattype cimport NPY_NAT
-from np_datetime cimport (npy_datetimestruct,
-                          dtstruct_to_dt64, dt64_to_dtstruct)
-from timezones import UTC
+from pandas._libs.tslibs.util cimport is_string_object, is_integer_object
+
+from pandas._libs.tslibs.ccalendar import MONTHS, DAYS
+from pandas._libs.tslibs.ccalendar cimport get_days_in_month, dayofweek
+from pandas._libs.tslibs.conversion cimport (
+    tz_convert_single, pydt_to_i8, localize_pydatetime)
+from pandas._libs.tslibs.nattype cimport NPY_NAT
+from pandas._libs.tslibs.np_datetime cimport (
+    npy_datetimestruct, dtstruct_to_dt64, dt64_to_dtstruct)
+from pandas._libs.tslibs.timezones import UTC
 
 # ---------------------------------------------------------------------
 # Constants
diff --git a/pandas/_libs/tslibs/parsing.pyx b/pandas/_libs/tslibs/parsing.pyx
index 6ec49e4fa92ff..37f11af81dfd6 100644
--- a/pandas/_libs/tslibs/parsing.pyx
+++ b/pandas/_libs/tslibs/parsing.pyx
@@ -27,8 +27,8 @@ from dateutil.relativedelta import relativedelta
 from dateutil.parser import DEFAULTPARSER
 from dateutil.parser import parse as du_parse
 
-from ccalendar import MONTH_NUMBERS
-from nattype import nat_strings, NaT
+from pandas._libs.tslibs.ccalendar import MONTH_NUMBERS
+from pandas._libs.tslibs.nattype import nat_strings, NaT
 
 # ----------------------------------------------------------------------
 # Constants
diff --git a/pandas/_libs/tslibs/period.pyx b/pandas/_libs/tslibs/period.pyx
index 7c7875f2a6a65..483b84940dbc8 100644
--- a/pandas/_libs/tslibs/period.pyx
+++ b/pandas/_libs/tslibs/period.pyx
@@ -20,37 +20,37 @@ from cpython.datetime cimport (PyDateTime_Check, PyDelta_Check, PyDate_Check,
 # import datetime C API
 PyDateTime_IMPORT
 
-from np_datetime cimport (npy_datetimestruct, dtstruct_to_dt64,
-                          dt64_to_dtstruct,
-                          pandas_datetime_to_datetimestruct,
-                          NPY_DATETIMEUNIT, NPY_FR_D)
+from pandas._libs.tslibs.np_datetime cimport (
+    npy_datetimestruct, dtstruct_to_dt64, dt64_to_dtstruct,
+    pandas_datetime_to_datetimestruct, NPY_DATETIMEUNIT, NPY_FR_D)
 
 cdef extern from "src/datetime/np_datetime.h":
     int64_t npy_datetimestruct_to_datetime(NPY_DATETIMEUNIT fr,
                                            npy_datetimestruct *d) nogil
 
-cimport util
-from util cimport is_period_object, is_string_object
-
-from timestamps import Timestamp
-from timezones cimport is_utc, is_tzlocal, get_dst_info
-from timedeltas import Timedelta
-from timedeltas cimport delta_to_nanoseconds
-
-cimport ccalendar
-from ccalendar cimport dayofweek, get_day_of_year, is_leapyear
-from ccalendar import MONTH_NUMBERS
-from conversion cimport tz_convert_utc_to_tzlocal
-from frequencies cimport (get_freq_code, get_base_alias,
-                          get_to_timestamp_base, get_freq_str,
-                          get_rule_month)
-from parsing import parse_time_string
-from resolution import Resolution
-from nattype import nat_strings
-from nattype cimport (
+cimport pandas._libs.tslibs.util as util
+from pandas._libs.tslibs.util cimport is_period_object, is_string_object
+
+from pandas._libs.tslibs.timestamps import Timestamp
+from pandas._libs.tslibs.timezones cimport is_utc, is_tzlocal, get_dst_info
+from pandas._libs.tslibs.timedeltas import Timedelta
+from pandas._libs.tslibs.timedeltas cimport delta_to_nanoseconds
+
+cimport pandas._libs.tslibs.ccalendar as ccalendar
+from pandas._libs.tslibs.ccalendar cimport (
+    dayofweek, get_day_of_year, is_leapyear)
+from pandas._libs.tslibs.ccalendar import MONTH_NUMBERS
+from pandas._libs.tslibs.conversion cimport tz_convert_utc_to_tzlocal
+from pandas._libs.tslibs.frequencies cimport (
+    get_freq_code, get_base_alias, get_to_timestamp_base, get_freq_str,
+    get_rule_month)
+from pandas._libs.tslibs.parsing import parse_time_string
+from pandas._libs.tslibs.resolution import Resolution
+from pandas._libs.tslibs.nattype import nat_strings
+from pandas._libs.tslibs.nattype cimport (
     _nat_scalar_rules, NPY_NAT, is_null_datetimelike, c_NaT as NaT)
-from offsets cimport to_offset
-from offsets import _Tick
+from pandas._libs.tslibs.offsets cimport to_offset
+from pandas._libs.tslibs.offsets import _Tick
 
 cdef bint PY2 = str == bytes
 cdef enum:
diff --git a/pandas/_libs/tslibs/resolution.pyx b/pandas/_libs/tslibs/resolution.pyx
index 3760c88a38c39..f80c1e9841abe 100644
--- a/pandas/_libs/tslibs/resolution.pyx
+++ b/pandas/_libs/tslibs/resolution.pyx
@@ -3,13 +3,15 @@
 import numpy as np
 from numpy cimport ndarray, int64_t, int32_t
 
-from util cimport is_string_object, get_nat
-
-from np_datetime cimport npy_datetimestruct, dt64_to_dtstruct
-from frequencies cimport get_freq_code
-from timezones cimport is_utc, is_tzlocal, maybe_get_tz, get_dst_info
-from conversion cimport tz_convert_utc_to_tzlocal
-from ccalendar cimport get_days_in_month
+from pandas._libs.tslibs.util cimport is_string_object, get_nat
+
+from pandas._libs.tslibs.np_datetime cimport (
+    npy_datetimestruct, dt64_to_dtstruct)
+from pandas._libs.tslibs.frequencies cimport get_freq_code
+from pandas._libs.tslibs.timezones cimport (
+    is_utc, is_tzlocal, maybe_get_tz, get_dst_info)
+from pandas._libs.tslibs.conversion cimport tz_convert_utc_to_tzlocal
+from pandas._libs.tslibs.ccalendar cimport get_days_in_month
 
 # ----------------------------------------------------------------------
 # Constants
diff --git a/pandas/_libs/tslibs/strptime.pyx b/pandas/_libs/tslibs/strptime.pyx
index 732caf1c0da7f..87658ae92175e 100644
--- a/pandas/_libs/tslibs/strptime.pyx
+++ b/pandas/_libs/tslibs/strptime.pyx
@@ -27,13 +27,13 @@ import numpy as np
 from numpy cimport int64_t
 
 
-from np_datetime cimport (check_dts_bounds,
-                          dtstruct_to_dt64, npy_datetimestruct)
+from pandas._libs.tslibs.np_datetime cimport (
+    check_dts_bounds, dtstruct_to_dt64, npy_datetimestruct)
 
-from util cimport is_string_object
+from pandas._libs.tslibs.util cimport is_string_object
 
-from nattype cimport checknull_with_nat, NPY_NAT
-from nattype import nat_strings
+from pandas._libs.tslibs.nattype cimport checknull_with_nat, NPY_NAT
+from pandas._libs.tslibs.nattype import nat_strings
 
 cdef dict _parse_code_table = {'y': 0,
                                'Y': 1,
diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index a03f460c9e2d2..037e7de27adc3 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -22,19 +22,20 @@ from cpython.datetime cimport (datetime, timedelta,
 PyDateTime_IMPORT
 
 
-cimport util
-from util cimport (is_timedelta64_object, is_datetime64_object,
-                   is_integer_object, is_float_object,
-                   is_string_object)
+cimport pandas._libs.tslibs.util as util
+from pandas._libs.tslibs.util cimport (
+    is_timedelta64_object, is_datetime64_object, is_integer_object,
+    is_float_object, is_string_object)
 
-from ccalendar import DAY_SECONDS
+from pandas._libs.tslibs.ccalendar import DAY_SECONDS
 
-from np_datetime cimport (cmp_scalar, reverse_ops, td64_to_tdstruct,
-                          pandas_timedeltastruct)
+from pandas._libs.tslibs.np_datetime cimport (
+    cmp_scalar, reverse_ops, td64_to_tdstruct, pandas_timedeltastruct)
 
-from nattype import nat_strings
-from nattype cimport checknull_with_nat, NPY_NAT, c_NaT as NaT
-from offsets cimport to_offset
+from pandas._libs.tslibs.nattype import nat_strings
+from pandas._libs.tslibs.nattype cimport (
+    checknull_with_nat, NPY_NAT, c_NaT as NaT)
+from pandas._libs.tslibs.offsets cimport to_offset
 
 # ----------------------------------------------------------------------
 # Constants
diff --git a/pandas/_libs/tslibs/timestamps.pxd b/pandas/_libs/tslibs/timestamps.pxd
index a162799828cba..b7282e02ff117 100644
--- a/pandas/_libs/tslibs/timestamps.pxd
+++ b/pandas/_libs/tslibs/timestamps.pxd
@@ -1,7 +1,7 @@
 # -*- coding: utf-8 -*-
 
 from numpy cimport int64_t
-from np_datetime cimport npy_datetimestruct
+from pandas._libs.tslibs.np_datetime cimport npy_datetimestruct
 
 cdef object create_timestamp_from_ts(int64_t value,
                                      npy_datetimestruct dts,
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index eda2b2fb6ca98..4761c7ff1f4eb 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -15,26 +15,29 @@ from cpython.datetime cimport (datetime,
                                PyDateTime_IMPORT)
 PyDateTime_IMPORT
 
-from util cimport (is_datetime64_object, is_timedelta64_object,
-                   is_integer_object, is_string_object, is_array,
-                   is_offset_object)
-
-cimport ccalendar
-from ccalendar import DAY_SECONDS
-from conversion import tz_localize_to_utc, normalize_i8_timestamps
-from conversion cimport (tz_convert_single, _TSObject,
-                         convert_to_tsobject, convert_datetime_to_tsobject)
-from fields import get_start_end_field, get_date_name_field
-from nattype cimport NPY_NAT, c_NaT as NaT
-from np_datetime import OutOfBoundsDatetime
-from np_datetime cimport (reverse_ops, cmp_scalar, check_dts_bounds,
-                          npy_datetimestruct, dt64_to_dtstruct)
-from offsets cimport to_offset
-from timedeltas import Timedelta
-from timedeltas cimport delta_to_nanoseconds
-from timezones cimport (
+from pandas._libs.tslibs.util cimport (
+    is_datetime64_object, is_timedelta64_object, is_integer_object,
+    is_string_object, is_array, is_offset_object)
+
+cimport pandas._libs.tslibs.ccalendar as ccalendar
+from pandas._libs.tslibs.ccalendar import DAY_SECONDS
+from pandas._libs.tslibs.conversion import (
+    tz_localize_to_utc, normalize_i8_timestamps)
+from pandas._libs.tslibs.conversion cimport (
+    tz_convert_single, _TSObject, convert_to_tsobject,
+    convert_datetime_to_tsobject)
+from pandas._libs.tslibs.fields import get_start_end_field, get_date_name_field
+from pandas._libs.tslibs.nattype cimport NPY_NAT, c_NaT as NaT
+from pandas._libs.tslibs.np_datetime import OutOfBoundsDatetime
+from pandas._libs.tslibs.np_datetime cimport (
+    reverse_ops, cmp_scalar, check_dts_bounds, npy_datetimestruct,
+    dt64_to_dtstruct)
+from pandas._libs.tslibs.offsets cimport to_offset
+from pandas._libs.tslibs.timedeltas import Timedelta
+from pandas._libs.tslibs.timedeltas cimport delta_to_nanoseconds
+from pandas._libs.tslibs.timezones cimport (
     get_timezone, is_utc, maybe_get_tz, treat_tz_as_pytz, tz_compare)
-from timezones import UTC
+from pandas._libs.tslibs.timezones import UTC
 
 # ----------------------------------------------------------------------
 # Constants
diff --git a/pandas/_libs/tslibs/timezones.pyx b/pandas/_libs/tslibs/timezones.pyx
index b67aab1452ebd..43a35d77dd127 100644
--- a/pandas/_libs/tslibs/timezones.pyx
+++ b/pandas/_libs/tslibs/timezones.pyx
@@ -19,7 +19,8 @@ from numpy cimport int64_t
 cnp.import_array()
 
 # ----------------------------------------------------------------------
-from util cimport is_string_object, is_integer_object, get_nat
+from pandas._libs.tslibs.util cimport (
+    is_string_object, is_integer_object, get_nat)
 
 cdef int64_t NPY_NAT = get_nat()
 
diff --git a/pandas/_libs/util.pxd b/pandas/_libs/util.pxd
index e05795d74c503..05a013ec0d7c9 100644
--- a/pandas/_libs/util.pxd
+++ b/pandas/_libs/util.pxd
@@ -1,4 +1,4 @@
-from tslibs.util cimport *
+from pandas._libs.tslibs.util cimport *
 
 from cython cimport Py_ssize_t
 
diff --git a/pandas/_libs/window.pyx b/pandas/_libs/window.pyx
index f517e0933264a..5f2c0233a0f13 100644
--- a/pandas/_libs/window.pyx
+++ b/pandas/_libs/window.pyx
@@ -19,12 +19,12 @@ cdef extern from "src/headers/cmath" namespace "std":
     int signbit(float64_t) nogil
     float64_t sqrt(float64_t x) nogil
 
-cimport util
-from util cimport numeric
+cimport pandas._libs.util as util
+from pandas._libs.util cimport numeric
 
-from skiplist cimport (skiplist_t,
-                       skiplist_init, skiplist_destroy,
-                       skiplist_get, skiplist_insert, skiplist_remove)
+from pandas._libs.skiplist cimport (
+    skiplist_t, skiplist_init, skiplist_destroy, skiplist_get, skiplist_insert,
+    skiplist_remove)
 
 cdef float32_t MINfloat32 = np.NINF
 cdef float64_t MINfloat64 = np.NINF