diff --git a/Lib/datetime.py b/Lib/datetime.py
index 0e64815944d..e35ee0554c1 100644
--- a/Lib/datetime.py
+++ b/Lib/datetime.py
@@ -733,7 +733,7 @@ class timedelta:
         if isinstance(other, timedelta):
             return self._cmp(other) == 0
         else:
-            return False
+            return NotImplemented
 
     def __le__(self, other):
         if isinstance(other, timedelta):
@@ -1310,7 +1310,7 @@ class time:
         if isinstance(other, time):
             return self._cmp(other, allow_mixed=True) == 0
         else:
-            return False
+            return NotImplemented
 
     def __le__(self, other):
         if isinstance(other, time):
diff --git a/Lib/test/datetimetester.py b/Lib/test/datetimetester.py
index 53de0658773..37ddd4b1a8b 100644
--- a/Lib/test/datetimetester.py
+++ b/Lib/test/datetimetester.py
@@ -53,6 +53,19 @@ OTHERSTUFF = (10, 34.5, "abc", {}, [], ())
 INF = float("inf")
 NAN = float("nan")
 
+
+class ComparesEqualClass(object):
+    """
+    A class that is always equal to whatever you compare it to.
+    """
+
+    def __eq__(self, other):
+        return True
+
+    def __ne__(self, other):
+        return False
+
+
 #############################################################################
 # module tests
 
@@ -399,6 +412,13 @@ class HarmlessMixedComparison:
         self.assertIn(me, [1, 20, [], me])
         self.assertIn([], [me, 1, 20, []])
 
+        # Comparison to objects of unsupported types should return
+        # NotImplemented which falls back to the right hand side's __eq__
+        # method. In this case, ComparesEqualClass.__eq__ always returns True.
+        # ComparesEqualClass.__ne__ always returns False.
+        self.assertTrue(me == ComparesEqualClass())
+        self.assertFalse(me != ComparesEqualClass())
+
     def test_harmful_mixed_comparison(self):
         me = self.theclass(1, 1, 1)
 
diff --git a/Misc/NEWS.d/next/Library/2019-07-13-10-59-43.bpo-37579.B1Tq9i.rst b/Misc/NEWS.d/next/Library/2019-07-13-10-59-43.bpo-37579.B1Tq9i.rst
new file mode 100644
index 00000000000..ad52cf2a06c
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-07-13-10-59-43.bpo-37579.B1Tq9i.rst
@@ -0,0 +1,4 @@
+Return :exc:`NotImplemented` in Python implementation of ``__eq__`` for
+:class:`~datetime.timedelta` and :class:`~datetime.time` when the other
+object being compared is not of the same type to match C implementation.
+Patch by Karthikeyan Singaravelan.