diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 7a10e8d1073d0..308748a1856d8 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -193,6 +193,7 @@ Other Enhancements
 - :func:`~DataFrame.to_csv`, :func:`~Series.to_csv`, :func:`~DataFrame.to_json`, and :func:`~Series.to_json` now support ``compression='infer'`` to infer compression based on filename extension (:issue:`15008`).
   The default compression for ``to_csv``, ``to_json``, and ``to_pickle`` methods has been updated to ``'infer'`` (:issue:`22004`).
 - :func:`to_timedelta` now supports iso-formated timedelta strings (:issue:`21877`)
+- Comparing :class:`Timedelta` with unknown types now return ``NotImplemented`` instead of ``False`` (:issue:`20829`)
 - :class:`Series` and :class:`DataFrame` now support :class:`Iterable` in constructor (:issue:`2193`)
 - :class:`DatetimeIndex` gained :attr:`DatetimeIndex.timetz` attribute. Returns local time with timezone information. (:issue:`21358`)
 - :meth:`round`, :meth:`ceil`, and meth:`floor` for :class:`DatetimeIndex` and :class:`Timestamp` now support an ``ambiguous`` argument for handling datetimes that are rounded to ambiguous times (:issue:`18946`)
@@ -1009,7 +1010,7 @@ Timedelta
 - Bug in :class:`TimedeltaIndex` incorrectly allowing indexing with ``Timestamp`` object (:issue:`20464`)
 - Fixed bug where subtracting :class:`Timedelta` from an object-dtyped array would raise ``TypeError`` (:issue:`21980`)
 - Fixed bug in adding a :class:`DataFrame` with all-`timedelta64[ns]` dtypes to a :class:`DataFrame` with all-integer dtypes returning incorrect results instead of raising ``TypeError`` (:issue:`22696`)
--
+
 
 Timezones
 ^^^^^^^^^
diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index 9c8be1901d1dc..b5b3abd01328c 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -724,27 +724,12 @@ cdef class _Timedelta(timedelta):
                     if is_timedelta64_object(other):
                         other = Timedelta(other)
                     else:
-                        if op == Py_EQ:
-                            return False
-                        elif op == Py_NE:
-                            return True
-
-                        # only allow ==, != ops
-                        raise TypeError('Cannot compare type {cls} with '
-                                        'type {other}'
-                                        .format(cls=type(self).__name__,
-                                                other=type(other).__name__))
+                        return NotImplemented
                 if util.is_array(other):
                     return PyObject_RichCompare(np.array([self]), other, op)
                 return PyObject_RichCompare(other, self, reverse_ops[op])
             else:
-                if op == Py_EQ:
-                    return False
-                elif op == Py_NE:
-                    return True
-                raise TypeError('Cannot compare type {cls} with type {other}'
-                                .format(cls=type(self).__name__,
-                                        other=type(other).__name__))
+                return NotImplemented
 
         return cmp_scalar(self.value, ots.value, op)
 
diff --git a/pandas/tests/scalar/timedelta/test_timedelta.py b/pandas/tests/scalar/timedelta/test_timedelta.py
index 017606dc42d59..0cac1119f76b5 100644
--- a/pandas/tests/scalar/timedelta/test_timedelta.py
+++ b/pandas/tests/scalar/timedelta/test_timedelta.py
@@ -42,8 +42,10 @@ def test_ops_error_str(self):
             with pytest.raises(TypeError):
                 left + right
 
-            with pytest.raises(TypeError):
-                left > right
+            # GH 20829: python 2 comparison naturally does not raise TypeError
+            if compat.PY3:
+                with pytest.raises(TypeError):
+                    left > right
 
             assert not left == right
             assert left != right
@@ -103,6 +105,55 @@ def test_compare_timedelta_ndarray(self):
         expected = np.array([False, False])
         tm.assert_numpy_array_equal(result, expected)
 
+    def test_compare_custom_object(self):
+        """Make sure non supported operations on Timedelta returns NonImplemented
+        and yields to other operand (GH20829)."""
+        class CustomClass(object):
+
+            def __init__(self, cmp_result=None):
+                self.cmp_result = cmp_result
+
+            def generic_result(self):
+                if self.cmp_result is None:
+                    return NotImplemented
+                else:
+                    return self.cmp_result
+
+            def __eq__(self, other):
+                return self.generic_result()
+
+            def __gt__(self, other):
+                return self.generic_result()
+
+        t = Timedelta('1s')
+
+        assert not (t == "string")
+        assert not (t == 1)
+        assert not (t == CustomClass())
+        assert not (t == CustomClass(cmp_result=False))
+
+        assert t < CustomClass(cmp_result=True)
+        assert not (t < CustomClass(cmp_result=False))
+
+        assert t == CustomClass(cmp_result=True)
+
+    @pytest.mark.skipif(compat.PY2,
+                        reason="python 2 does not raise TypeError for \
+                               comparisons of different types")
+    @pytest.mark.parametrize("val", [
+        "string", 1])
+    def test_compare_unknown_type(self, val):
+        # GH20829
+        t = Timedelta('1s')
+        with pytest.raises(TypeError):
+            t >= val
+        with pytest.raises(TypeError):
+            t > val
+        with pytest.raises(TypeError):
+            t <= val
+        with pytest.raises(TypeError):
+            t < val
+
 
 class TestTimedeltas(object):