diff --git a/doc/source/whatsnew/v0.17.0.txt b/doc/source/whatsnew/v0.17.0.txt
index 18c39ccf820eb..3af9c887bb82f 100644
--- a/doc/source/whatsnew/v0.17.0.txt
+++ b/doc/source/whatsnew/v0.17.0.txt
@@ -629,6 +629,7 @@ Bug Fixes
 - Bug that caused segfault when resampling an empty Series (:issue:`10228`)
 - Bug in ``DatetimeIndex`` and ``PeriodIndex.value_counts`` resets name from its result, but retains in result's ``Index``. (:issue:`10150`)
 - Bug in ``pd.eval`` using ``numexpr`` engine coerces 1 element numpy array to scalar (:issue:`10546`)
+- Bug in ``PeriodIndex.__contains__`` & ``DatetimeIndex.__contains__`` that always returned False for each other's objects (:issue:`10798`)
 - Bug in ``pd.concat`` with ``axis=0`` when column is of dtype ``category`` (:issue:`10177`)
 - Bug in ``read_msgpack`` where input type is not always checked (:issue:`10369`, :issue:`10630`)
 - Bug in ``pd.read_csv`` with kwargs ``index_col=False``, ``index_col=['a', 'b']`` or ``dtype``
diff --git a/pandas/tests/test_index.py b/pandas/tests/test_index.py
index 9a3576a8fd846..52d2d85bda739 100644
--- a/pandas/tests/test_index.py
+++ b/pandas/tests/test_index.py
@@ -2817,7 +2817,31 @@ def test_view(self):
         result = self._holder(i)
         tm.assert_index_equal(result, i)
 
-class TestDatetimeIndex(DatetimeLike, tm.TestCase):
+class DatetimeAbsoluteLike(DatetimeLike):
+
+    # GH10801
+    def test_datetimeabsolute_contains(self):
+
+        i = self.create_index()
+
+        self.assertTrue(i[2] in i)
+        self.assertFalse('2012' in i)
+
+        #  python datetime objects
+        self.assertTrue(datetime(2013,1,1) in i)
+
+        # strings
+        self.assertTrue('2013-1-1' in i)
+
+        # Timestamp # GH10801
+        self.assertTrue(pd.Timestamp('2013-1-1') in i)
+
+        # pandas Period
+        self.assertTrue(pd.Period('2013-1-1', 'D') in i)
+        self.assertFalse(pd.Period('2013-1-1', 'M') in i)
+
+
+class TestDatetimeIndex(DatetimeAbsoluteLike, tm.TestCase):
     _holder = DatetimeIndex
     _multiprocess_can_split_ = True
 
@@ -2964,7 +2988,7 @@ def test_nat(self):
         self.assertIs(DatetimeIndex([np.nan])[0], pd.NaT)
 
 
-class TestPeriodIndex(DatetimeLike, tm.TestCase):
+class TestPeriodIndex(DatetimeAbsoluteLike, tm.TestCase):
     _holder = PeriodIndex
     _multiprocess_can_split_ = True
 
diff --git a/pandas/tseries/index.py b/pandas/tseries/index.py
index 19ff9a4b19a3e..8605058e3ec32 100644
--- a/pandas/tseries/index.py
+++ b/pandas/tseries/index.py
@@ -1289,6 +1289,12 @@ def get_loc(self, key, method=None):
                                           'when key is a time object')
             return self.indexer_at_time(key)
 
+        # check if it's a Period and the frequencies are the same - otherwise a monthly period would match for
+        # a daily timestamp at the beginning of the month. NB: 'B' and 'D' therefore won't match
+        if isinstance(key, com.ABCPeriod) and key.freq == self.freq:
+            key =  key.to_timestamp()
+            return Index.get_loc(self, key, method=method)
+
         try:
             return Index.get_loc(self, key, method=method)
         except (KeyError, ValueError, TypeError):
diff --git a/pandas/tseries/period.py b/pandas/tseries/period.py
index e7b229e91cbc8..62289219ad72e 100644
--- a/pandas/tseries/period.py
+++ b/pandas/tseries/period.py
@@ -296,14 +296,14 @@ def _na_value(self):
         return self._box_func(tslib.iNaT)
 
     def __contains__(self, key):
+        # if key isn't a Period of the same freq, rely on `get_loc` for the coercion.
         if not isinstance(key, Period) or key.freq != self.freq:
-            if isinstance(key, compat.string_types):
-                try:
-                    self.get_loc(key)
-                    return True
-                except Exception:
-                    return False
-            return False
+            try:
+                self.get_loc(key)
+                return True
+            except Exception:
+                return False
+        # If it is a Period of the same freq, go straight to the _engine
         return key.ordinal in self._engine
 
     @property