diff --git a/doc/source/whatsnew/v0.16.1.txt b/doc/source/whatsnew/v0.16.1.txt
index 9f989b2cf0ea9..d0f7af2275812 100644
--- a/doc/source/whatsnew/v0.16.1.txt
+++ b/doc/source/whatsnew/v0.16.1.txt
@@ -30,6 +30,7 @@ Enhancements
     df = DataFrame(np.random.randn(3, 3), columns=['A', 'B', 'C'])
     df.drop(['A', 'X'], axis=1, errors='ignore')
 
+- Allow conversion of values with dtype ``datetime64`` or ``timedelta64`` to strings using ``astype(str)`` (:issue:`9757`)
 
 .. _whatsnew_0161.api:
 
diff --git a/pandas/core/common.py b/pandas/core/common.py
index ec805aba34d48..0fb35c2fb02fc 100644
--- a/pandas/core/common.py
+++ b/pandas/core/common.py
@@ -2637,7 +2637,12 @@ def _astype_nansafe(arr, dtype, copy=True):
     if not isinstance(dtype, np.dtype):
         dtype = _coerce_to_dtype(dtype)
 
-    if is_datetime64_dtype(arr):
+    if issubclass(dtype.type, compat.text_type):
+        # in Py3 that's str, in Py2 that's unicode
+        return lib.astype_unicode(arr.ravel()).reshape(arr.shape)
+    elif issubclass(dtype.type, compat.string_types):
+        return lib.astype_str(arr.ravel()).reshape(arr.shape)
+    elif is_datetime64_dtype(arr):
         if dtype == object:
             return tslib.ints_to_pydatetime(arr.view(np.int64))
         elif dtype == np.int64:
@@ -2675,11 +2680,6 @@ def _astype_nansafe(arr, dtype, copy=True):
     elif arr.dtype == np.object_ and np.issubdtype(dtype.type, np.integer):
         # work around NumPy brokenness, #1987
         return lib.astype_intsafe(arr.ravel(), dtype).reshape(arr.shape)
-    elif issubclass(dtype.type, compat.text_type):
-        # in Py3 that's str, in Py2 that's unicode
-        return lib.astype_unicode(arr.ravel()).reshape(arr.shape)
-    elif issubclass(dtype.type, compat.string_types):
-        return lib.astype_str(arr.ravel()).reshape(arr.shape)
 
     if copy:
         return arr.astype(dtype)
diff --git a/pandas/tests/test_frame.py b/pandas/tests/test_frame.py
index b8bdd2d4e3b40..6ea76710b4de7 100644
--- a/pandas/tests/test_frame.py
+++ b/pandas/tests/test_frame.py
@@ -4192,6 +4192,30 @@ def test_astype_cast_nan_int(self):
         df = DataFrame(data={"Values": [1.0, 2.0, 3.0, np.nan]})
         self.assertRaises(ValueError, df.astype, np.int64)
 
+    def test_astype_str(self):
+        # GH9757
+        a = Series(date_range('2010-01-04', periods=5))
+        b = Series(date_range('3/6/2012 00:00', periods=5, tz='US/Eastern'))
+        c = Series([Timedelta(x, unit='d') for x in range(5)])
+        d = Series(range(5))
+        e = Series([0.0, 0.2, 0.4, 0.6, 0.8])
+
+        df = DataFrame({'a' : a, 'b' : b, 'c' : c, 'd' : d, 'e' : e})
+
+        # Test str and unicode on python 2.x and just str on python 3.x
+        for tt in set([str, compat.text_type]):
+            result = df.astype(tt)
+
+            expected = DataFrame({
+                'a' : list(map(tt, a.values)),
+                'b' : list(map(tt, b.values)),
+                'c' : list(map(tt, c.values)),
+                'd' : list(map(tt, d.values)),
+                'e' : list(map(tt, e.values)),
+                })
+
+            assert_frame_equal(result, expected)
+
     def test_array_interface(self):
         result = np.sqrt(self.frame)
         tm.assert_isinstance(result, type(self.frame))
diff --git a/pandas/tests/test_series.py b/pandas/tests/test_series.py
index f044fe540ea24..fec98a37b5017 100644
--- a/pandas/tests/test_series.py
+++ b/pandas/tests/test_series.py
@@ -5511,6 +5511,24 @@ def test_astype_str(self):
                 expec = s.map(compat.text_type)
                 assert_series_equal(res, expec)
 
+        # GH9757
+        # Test str and unicode on python 2.x and just str on python 3.x
+        for tt in set([str, compat.text_type]):
+            ts = Series([Timestamp('2010-01-04 00:00:00')])
+            s = ts.astype(tt)
+            expected = Series([tt(ts.values[0])])
+            assert_series_equal(s, expected)
+
+            ts = Series([Timestamp('2010-01-04 00:00:00', tz='US/Eastern')])
+            s = ts.astype(tt)
+            expected = Series([tt(ts.values[0])])
+            assert_series_equal(s, expected)
+
+            td = Series([Timedelta(1, unit='d')])
+            s = td.astype(tt)
+            expected = Series([tt(td.values[0])])
+            assert_series_equal(s, expected)
+
     def test_astype_unicode(self):
 
         # GH7758