diff --git a/doc/source/v0.15.0.txt b/doc/source/v0.15.0.txt
index 06c93541a7783..086c24246918d 100644
--- a/doc/source/v0.15.0.txt
+++ b/doc/source/v0.15.0.txt
@@ -198,6 +198,10 @@ Bug Fixes
 - Bug in ``DataFrame.as_matrix()`` with mixed ``datetime64[ns]`` and ``timedelta64[ns]`` dtypes (:issue:`7778`)
 - Bug in ``HDFStore.select_column()`` not preserving UTC timezone info when selecting a DatetimeIndex (:issue:`7777`)
 
+- Bug in ``DatetimeIndex`` and ``PeriodIndex`` in-place addition and subtraction cause different result from normal one (:issue:`6527`)
+- Bug in adding and subtracting ``PeriodIndex`` with ``PeriodIndex`` raise ``TypeError`` (:issue:`7741`)
+- Bug in ``combine_first`` with ``PeriodIndex`` data raises ``TypeError`` (:issue:`3367`)
+
 
 - Bug in pickles contains ``DateOffset`` may raise ``AttributeError`` when ``normalize`` attribute is reffered internally (:issue:`7748`)
 
diff --git a/pandas/core/base.py b/pandas/core/base.py
index 4035627b98458..243e34e35784a 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -1,6 +1,8 @@
 """
 Base and utility classes for pandas objects.
 """
+import datetime
+
 from pandas import compat
 import numpy as np
 from pandas.core import common as com
@@ -511,4 +513,34 @@ def resolution(self):
         from pandas.tseries.frequencies import get_reso_string
         return get_reso_string(self._resolution)
 
+    def __add__(self, other):
+        from pandas.core.index import Index
+        from pandas.tseries.offsets import DateOffset
+        if isinstance(other, Index):
+            return self.union(other)
+        elif isinstance(other, (DateOffset, datetime.timedelta, np.timedelta64)):
+            return self._add_delta(other)
+        elif com.is_integer(other):
+            return self.shift(other)
+        else:  # pragma: no cover
+            return NotImplemented
+
+    def __sub__(self, other):
+        from pandas.core.index import Index
+        from pandas.tseries.offsets import DateOffset
+        if isinstance(other, Index):
+            return self.diff(other)
+        elif isinstance(other, (DateOffset, datetime.timedelta, np.timedelta64)):
+            return self._add_delta(-other)
+        elif com.is_integer(other):
+            return self.shift(-other)
+        else:  # pragma: no cover
+            return NotImplemented
+
+    __iadd__ = __add__
+    __isub__ = __sub__
+
+    def _add_delta(self, other):
+        return NotImplemented
+
 
diff --git a/pandas/tests/test_base.py b/pandas/tests/test_base.py
index 761d79a288df3..1b7db1451f6cf 100644
--- a/pandas/tests/test_base.py
+++ b/pandas/tests/test_base.py
@@ -481,6 +481,8 @@ def test_factorize(self):
 
 class TestDatetimeIndexOps(Ops):
     _allowed = '_allow_datetime_index_ops'
+    tz = [None, 'UTC', 'Asia/Tokyo', 'US/Eastern',
+          'dateutil/Asia/Singapore', 'dateutil/US/Pacific']
 
     def setUp(self):
         super(TestDatetimeIndexOps, self).setUp()
@@ -545,7 +547,7 @@ def test_asobject_tolist(self):
         self.assertEqual(idx.tolist(), expected_list)
 
     def test_minmax(self):
-        for tz in [None, 'Asia/Tokyo', 'US/Eastern']:
+        for tz in self.tz:
             # monotonic
             idx1 = pd.DatetimeIndex([pd.NaT, '2011-01-01', '2011-01-02',
                                      '2011-01-03'], tz=tz)
@@ -613,6 +615,100 @@ def test_resolution(self):
                 idx = pd.date_range(start='2013-04-01', periods=30, freq=freq, tz=tz)
                 self.assertEqual(idx.resolution, expected)
 
+    def test_add_iadd(self):
+        for tz in self.tz:
+            # union
+            rng1 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+            other1 = pd.date_range('1/6/2000', freq='D', periods=5, tz=tz)
+            expected1 = pd.date_range('1/1/2000', freq='D', periods=10, tz=tz)
+
+            rng2 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+            other2 = pd.date_range('1/4/2000', freq='D', periods=5, tz=tz)
+            expected2 = pd.date_range('1/1/2000', freq='D', periods=8, tz=tz)
+
+            rng3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+            other3 = pd.DatetimeIndex([], tz=tz)
+            expected3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+
+            for rng, other, expected in [(rng1, other1, expected1), (rng2, other2, expected2),
+                                         (rng3, other3, expected3)]:
+                result_add = rng + other
+                result_union = rng.union(other)
+
+                tm.assert_index_equal(result_add, expected)
+                tm.assert_index_equal(result_union, expected)
+                rng += other
+                tm.assert_index_equal(rng, expected)
+
+            # offset
+            if _np_version_under1p7:
+                offsets = [pd.offsets.Hour(2), timedelta(hours=2)]
+            else:
+                offsets = [pd.offsets.Hour(2), timedelta(hours=2), np.timedelta64(2, 'h')]
+
+            for delta in offsets:
+                rng = pd.date_range('2000-01-01', '2000-02-01', tz=tz)
+                result = rng + delta
+                expected = pd.date_range('2000-01-01 02:00', '2000-02-01 02:00', tz=tz)
+                tm.assert_index_equal(result, expected)
+                rng += delta
+                tm.assert_index_equal(rng, expected)
+
+            # int
+            rng = pd.date_range('2000-01-01 09:00', freq='H', periods=10, tz=tz)
+            result = rng + 1
+            expected = pd.date_range('2000-01-01 10:00', freq='H', periods=10, tz=tz)
+            tm.assert_index_equal(result, expected)
+            rng += 1
+            tm.assert_index_equal(rng, expected)
+
+    def test_sub_isub(self):
+        for tz in self.tz:
+            # diff
+            rng1 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+            other1 = pd.date_range('1/6/2000', freq='D', periods=5, tz=tz)
+            expected1 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+
+            rng2 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+            other2 = pd.date_range('1/4/2000', freq='D', periods=5, tz=tz)
+            expected2 = pd.date_range('1/1/2000', freq='D', periods=3, tz=tz)
+
+            rng3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+            other3 = pd.DatetimeIndex([], tz=tz)
+            expected3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+
+            for rng, other, expected in [(rng1, other1, expected1), (rng2, other2, expected2),
+                                         (rng3, other3, expected3)]:
+                result_add = rng - other
+                result_union = rng.diff(other)
+
+                tm.assert_index_equal(result_add, expected)
+                tm.assert_index_equal(result_union, expected)
+                rng -= other
+                tm.assert_index_equal(rng, expected)
+
+            # offset
+            if _np_version_under1p7:
+                offsets = [pd.offsets.Hour(2), timedelta(hours=2)]
+            else:
+                offsets = [pd.offsets.Hour(2), timedelta(hours=2), np.timedelta64(2, 'h')]
+
+            for delta in offsets:
+                rng = pd.date_range('2000-01-01', '2000-02-01', tz=tz)
+                result = rng - delta
+                expected = pd.date_range('1999-12-31 22:00', '2000-01-31 22:00', tz=tz)
+                tm.assert_index_equal(result, expected)
+                rng -= delta
+                tm.assert_index_equal(rng, expected)
+
+            # int
+            rng = pd.date_range('2000-01-01 09:00', freq='H', periods=10, tz=tz)
+            result = rng - 1
+            expected = pd.date_range('2000-01-01 08:00', freq='H', periods=10, tz=tz)
+            tm.assert_index_equal(result, expected)
+            rng -= 1
+            tm.assert_index_equal(rng, expected)
+
 
 class TestPeriodIndexOps(Ops):
     _allowed = '_allow_period_index_ops'
@@ -745,6 +841,133 @@ def test_resolution(self):
             idx = pd.period_range(start='2013-04-01', periods=30, freq=freq)
             self.assertEqual(idx.resolution, expected)
 
+    def test_add_iadd(self):
+        # union
+        rng1 = pd.period_range('1/1/2000', freq='D', periods=5)
+        other1 = pd.period_range('1/6/2000', freq='D', periods=5)
+        expected1 = pd.period_range('1/1/2000', freq='D', periods=10)
+
+        rng2 = pd.period_range('1/1/2000', freq='D', periods=5)
+        other2 = pd.period_range('1/4/2000', freq='D', periods=5)
+        expected2 = pd.period_range('1/1/2000', freq='D', periods=8)
+
+        rng3 = pd.period_range('1/1/2000', freq='D', periods=5)
+        other3 = pd.PeriodIndex([], freq='D')
+        expected3 = pd.period_range('1/1/2000', freq='D', periods=5)
+
+        rng4 = pd.period_range('2000-01-01 09:00', freq='H', periods=5)
+        other4 = pd.period_range('2000-01-02 09:00', freq='H', periods=5)
+        expected4 = pd.PeriodIndex(['2000-01-01 09:00', '2000-01-01 10:00',
+                                    '2000-01-01 11:00', '2000-01-01 12:00',
+                                    '2000-01-01 13:00', '2000-01-02 09:00',
+                                    '2000-01-02 10:00', '2000-01-02 11:00',
+                                    '2000-01-02 12:00', '2000-01-02 13:00'],
+                                   freq='H')
+
+        rng5 = pd.PeriodIndex(['2000-01-01 09:01', '2000-01-01 09:03',
+                               '2000-01-01 09:05'], freq='T')
+        other5 = pd.PeriodIndex(['2000-01-01 09:01', '2000-01-01 09:05'
+                                 '2000-01-01 09:08'], freq='T')
+        expected5 = pd.PeriodIndex(['2000-01-01 09:01', '2000-01-01 09:03',
+                                    '2000-01-01 09:05', '2000-01-01 09:08'],
+                                   freq='T')
+
+        rng6 = pd.period_range('2000-01-01', freq='M', periods=7)
+        other6 = pd.period_range('2000-04-01', freq='M', periods=7)
+        expected6 = pd.period_range('2000-01-01', freq='M', periods=10)
+
+        rng7 = pd.period_range('2003-01-01', freq='A', periods=5)
+        other7 = pd.period_range('1998-01-01', freq='A', periods=8)
+        expected7 = pd.period_range('1998-01-01', freq='A', periods=10)
+
+        for rng, other, expected in [(rng1, other1, expected1), (rng2, other2, expected2),
+                                     (rng3, other3, expected3), (rng4, other4, expected4),
+                                     (rng5, other5, expected5), (rng6, other6, expected6),
+                                     (rng7, other7, expected7)]:
+
+            result_add = rng + other
+            result_union = rng.union(other)
+
+            tm.assert_index_equal(result_add, expected)
+            tm.assert_index_equal(result_union, expected)
+            # GH 6527
+            rng += other
+            tm.assert_index_equal(rng, expected)
+
+        # offset
+        for delta in [pd.offsets.Hour(2), timedelta(hours=2)]:
+            rng = pd.period_range('2000-01-01', '2000-02-01')
+            with tm.assertRaisesRegexp(TypeError, 'unsupported operand type\(s\)'):
+                result = rng + delta
+            with tm.assertRaisesRegexp(TypeError, 'unsupported operand type\(s\)'):
+                rng += delta
+
+        # int
+        rng = pd.period_range('2000-01-01 09:00', freq='H', periods=10)
+        result = rng + 1
+        expected = pd.period_range('2000-01-01 10:00', freq='H', periods=10)
+        tm.assert_index_equal(result, expected)
+        rng += 1
+        tm.assert_index_equal(rng, expected)
+
+    def test_sub_isub(self):
+        # diff
+        rng1 = pd.period_range('1/1/2000', freq='D', periods=5)
+        other1 = pd.period_range('1/6/2000', freq='D', periods=5)
+        expected1 = pd.period_range('1/1/2000', freq='D', periods=5)
+
+        rng2 = pd.period_range('1/1/2000', freq='D', periods=5)
+        other2 = pd.period_range('1/4/2000', freq='D', periods=5)
+        expected2 = pd.period_range('1/1/2000', freq='D', periods=3)
+
+        rng3 = pd.period_range('1/1/2000', freq='D', periods=5)
+        other3 = pd.PeriodIndex([], freq='D')
+        expected3 = pd.period_range('1/1/2000', freq='D', periods=5)
+
+        rng4 = pd.period_range('2000-01-01 09:00', freq='H', periods=5)
+        other4 = pd.period_range('2000-01-02 09:00', freq='H', periods=5)
+        expected4 = rng4
+
+        rng5 = pd.PeriodIndex(['2000-01-01 09:01', '2000-01-01 09:03',
+                               '2000-01-01 09:05'], freq='T')
+        other5 = pd.PeriodIndex(['2000-01-01 09:01', '2000-01-01 09:05'], freq='T')
+        expected5 = pd.PeriodIndex(['2000-01-01 09:03'], freq='T')
+
+        rng6 = pd.period_range('2000-01-01', freq='M', periods=7)
+        other6 = pd.period_range('2000-04-01', freq='M', periods=7)
+        expected6 = pd.period_range('2000-01-01', freq='M', periods=3)
+
+        rng7 = pd.period_range('2003-01-01', freq='A', periods=5)
+        other7 = pd.period_range('1998-01-01', freq='A', periods=8)
+        expected7 = pd.period_range('2006-01-01', freq='A', periods=2)
+
+        for rng, other, expected in [(rng1, other1, expected1), (rng2, other2, expected2),
+                                     (rng3, other3, expected3), (rng4, other4, expected4),
+                                     (rng5, other5, expected5), (rng6, other6, expected6),
+                                     (rng7, other7, expected7),]:
+            result_add = rng - other
+            result_union = rng.diff(other)
+
+            tm.assert_index_equal(result_add, expected)
+            tm.assert_index_equal(result_union, expected)
+            rng -= other
+            tm.assert_index_equal(rng, expected)
+
+        # offset
+        for delta in [pd.offsets.Hour(2), timedelta(hours=2)]:
+            with tm.assertRaisesRegexp(TypeError, 'unsupported operand type\(s\)'):
+                result = rng + delta
+            with tm.assertRaisesRegexp(TypeError, 'unsupported operand type\(s\)'):
+                rng += delta
+
+        # int
+        rng = pd.period_range('2000-01-01 09:00', freq='H', periods=10)
+        result = rng - 1
+        expected = pd.period_range('2000-01-01 08:00', freq='H', periods=10)
+        tm.assert_index_equal(result, expected)
+        rng -= 1
+        tm.assert_index_equal(rng, expected)
+
 
 if __name__ == '__main__':
     import nose
diff --git a/pandas/tseries/index.py b/pandas/tseries/index.py
index 9423037844e74..2a3c53135a644 100644
--- a/pandas/tseries/index.py
+++ b/pandas/tseries/index.py
@@ -595,30 +595,6 @@ def __setstate__(self, state):
         else:  # pragma: no cover
             np.ndarray.__setstate__(self, state)
 
-    def __add__(self, other):
-        if isinstance(other, Index):
-            return self.union(other)
-        elif isinstance(other, (DateOffset, timedelta)):
-            return self._add_delta(other)
-        elif isinstance(other, np.timedelta64):
-            return self._add_delta(other)
-        elif com.is_integer(other):
-            return self.shift(other)
-        else:  # pragma: no cover
-            raise TypeError(other)
-
-    def __sub__(self, other):
-        if isinstance(other, Index):
-            return self.diff(other)
-        elif isinstance(other, (DateOffset, timedelta)):
-            return self._add_delta(-other)
-        elif isinstance(other, np.timedelta64):
-            return self._add_delta(-other)
-        elif com.is_integer(other):
-            return self.shift(-other)
-        else:  # pragma: no cover
-            raise TypeError(other)
-
     def _add_delta(self, delta):
         if isinstance(delta, (Tick, timedelta)):
             inc = offsets._delta_to_nanoseconds(delta)
diff --git a/pandas/tseries/period.py b/pandas/tseries/period.py
index 8c4bb2f5adc5e..887bf806dd4e4 100644
--- a/pandas/tseries/period.py
+++ b/pandas/tseries/period.py
@@ -872,19 +872,6 @@ def shift(self, n):
         values[mask] = tslib.iNaT
         return PeriodIndex(data=values, name=self.name, freq=self.freq)
 
-    def __add__(self, other):
-        try:
-            return self.shift(other)
-        except TypeError:
-            # self.values + other raises TypeError for invalid input
-            return NotImplemented
-
-    def __sub__(self, other):
-        try:
-            return self.shift(-other)
-        except TypeError:
-            return NotImplemented
-
     @property
     def inferred_type(self):
         # b/c data is represented as ints make sure we can't have ambiguous
diff --git a/pandas/tseries/tests/test_period.py b/pandas/tseries/tests/test_period.py
index 53375b4d07796..f5f66a49c29d4 100644
--- a/pandas/tseries/tests/test_period.py
+++ b/pandas/tseries/tests/test_period.py
@@ -2450,6 +2450,20 @@ def test_recreate_from_data(self):
             idx = PeriodIndex(org.values, freq=o)
             self.assertTrue(idx.equals(org))
 
+    def test_combine_first(self):
+        # GH 3367
+        didx = pd.DatetimeIndex(start='1950-01-31', end='1950-07-31', freq='M')
+        pidx = pd.PeriodIndex(start=pd.Period('1950-1'), end=pd.Period('1950-7'), freq='M')
+        # check to be consistent with DatetimeIndex
+        for idx in [didx, pidx]:
+            a = pd.Series([1, np.nan, np.nan, 4, 5, np.nan, 7], index=idx)
+            b = pd.Series([9, 9, 9, 9, 9, 9, 9], index=idx)
+
+            result = a.combine_first(b)
+            expected = pd.Series([1, 9, 9, 4, 5, 9, 7], index=idx, dtype=np.float64)
+            tm.assert_series_equal(result, expected)
+
+
 def _permute(obj):
     return obj.take(np.random.permutation(len(obj)))
 
diff --git a/pandas/tseries/tests/test_timeseries.py b/pandas/tseries/tests/test_timeseries.py
index b6761426edc5d..f2bc66f156c75 100644
--- a/pandas/tseries/tests/test_timeseries.py
+++ b/pandas/tseries/tests/test_timeseries.py
@@ -1235,13 +1235,6 @@ def test_last_subset(self):
         result = ts[:0].last('3M')
         assert_series_equal(result, ts[:0])
 
-    def test_add_offset(self):
-        rng = date_range('1/1/2000', '2/1/2000')
-
-        result = rng + offsets.Hour(2)
-        expected = date_range('1/1/2000 02:00', '2/1/2000 02:00')
-        self.assertTrue(result.equals(expected))
-
     def test_format_pre_1900_dates(self):
         rng = date_range('1/1/1850', '1/1/1950', freq='A-DEC')
         rng.format()
@@ -2314,14 +2307,6 @@ def test_map(self):
         exp = [f(x) for x in rng]
         self.assert_numpy_array_equal(result, exp)
 
-    def test_add_union(self):
-        rng = date_range('1/1/2000', periods=5)
-        rng2 = date_range('1/6/2000', periods=5)
-
-        result = rng + rng2
-        expected = rng.union(rng2)
-        self.assertTrue(result.equals(expected))
-
     def test_misc_coverage(self):
         rng = date_range('1/1/2000', periods=5)
         result = rng.groupby(rng.day)