diff --git a/python/cudf/cudf/core/column/datetime.py b/python/cudf/cudf/core/column/datetime.py
index 8073092775d..da6c4fb858c 100644
--- a/python/cudf/cudf/core/column/datetime.py
+++ b/python/cudf/cudf/core/column/datetime.py
@@ -460,14 +460,22 @@ def _binaryop(self, other: ColumnBinaryOperand, op: str) -> ColumnBase:
             if isinstance(other, ColumnBase) and not isinstance(
                 other, DatetimeColumn
             ):
-                return _all_bools_with_nulls(
+                result = _all_bools_with_nulls(
                     self, other, bool_fill_value=op == "__ne__"
                 )
+                if cudf.get_option("mode.pandas_compatible"):
+                    result = result.fillna(op == "__ne__")
+                return result
 
         if out_dtype is None:
             return NotImplemented
 
-        return libcudf.binaryop.binaryop(lhs, rhs, op, out_dtype)
+        result = libcudf.binaryop.binaryop(lhs, rhs, op, out_dtype)
+        if cudf.get_option(
+            "mode.pandas_compatible"
+        ) and out_dtype == cudf.dtype(np.bool_):
+            result = result.fillna(op == "__ne__")
+        return result
 
     def fillna(
         self,
diff --git a/python/cudf/cudf/core/column/timedelta.py b/python/cudf/cudf/core/column/timedelta.py
index b571461b307..e254761e9ec 100644
--- a/python/cudf/cudf/core/column/timedelta.py
+++ b/python/cudf/cudf/core/column/timedelta.py
@@ -181,7 +181,7 @@ def _binaryop(self, other: ColumnBinaryOperand, op: str) -> ColumnBase:
                 "__ge__",
                 "NULL_EQUALS",
             }:
-                out_dtype = np.bool_
+                out_dtype = cudf.dtype(np.bool_)
             elif op == "__mod__":
                 out_dtype = determine_out_dtype(self.dtype, other.dtype)
             elif op in {"__truediv__", "__floordiv__"}:
@@ -206,16 +206,24 @@ def _binaryop(self, other: ColumnBinaryOperand, op: str) -> ColumnBase:
                 if isinstance(other, ColumnBase) and not isinstance(
                     other, TimeDeltaColumn
                 ):
-                    return _all_bools_with_nulls(
+                    result = _all_bools_with_nulls(
                         self, other, bool_fill_value=op == "__ne__"
                     )
+                    if cudf.get_option("mode.pandas_compatible"):
+                        result = result.fillna(op == "__ne__")
+                    return result
 
         if out_dtype is None:
             return NotImplemented
 
         lhs, rhs = (other, this) if reflect else (this, other)
 
-        return libcudf.binaryop.binaryop(lhs, rhs, op, out_dtype)
+        result = libcudf.binaryop.binaryop(lhs, rhs, op, out_dtype)
+        if cudf.get_option(
+            "mode.pandas_compatible"
+        ) and out_dtype == cudf.dtype(np.bool_):
+            result = result.fillna(op == "__ne__")
+        return result
 
     def normalize_binop_value(self, other) -> ColumnBinaryOperand:
         if isinstance(other, (ColumnBase, cudf.Scalar)):
diff --git a/python/cudf/cudf/tests/test_datetime.py b/python/cudf/cudf/tests/test_datetime.py
index a59f8b62e7e..4c4657ccba1 100644
--- a/python/cudf/cudf/tests/test_datetime.py
+++ b/python/cudf/cudf/tests/test_datetime.py
@@ -2109,6 +2109,27 @@ def test_datetime_binop_tz_timestamp(op):
         op(s, date_scalar)
 
 
+@pytest.mark.parametrize(
+    "data1", [["20110101", "20120101", None, "20140101", None]]
+)
+@pytest.mark.parametrize(
+    "data2", [["20110101", "20120101", "20130101", None, None]]
+)
+@pytest.mark.parametrize("op", _cmpops)
+def test_datetime_series_cmpops_pandas_compatibility(data1, data2, op):
+    gsr1 = cudf.Series(data=data1, dtype="datetime64[ns]")
+    psr1 = gsr1.to_pandas()
+
+    gsr2 = cudf.Series(data=data2, dtype="datetime64[ns]")
+    psr2 = gsr2.to_pandas()
+
+    expect = op(psr1, psr2)
+    with cudf.option_context("mode.pandas_compatible", True):
+        got = op(gsr1, gsr2)
+
+    assert_eq(expect, got)
+
+
 def test_datetime_getitem_na():
     s = cudf.Series([1, 2, None, 3], dtype="datetime64[ns]")
     assert s[2] is cudf.NaT
diff --git a/python/cudf/cudf/tests/test_timedelta.py b/python/cudf/cudf/tests/test_timedelta.py
index 681b42fd3bd..ef39a4fef5a 100644
--- a/python/cudf/cudf/tests/test_timedelta.py
+++ b/python/cudf/cudf/tests/test_timedelta.py
@@ -57,6 +57,15 @@
     [12, 11, 2.32, 2234.32411, 2343.241, 23432.4, 23234],
 ]
 
+_cmpops = [
+    operator.lt,
+    operator.gt,
+    operator.le,
+    operator.ge,
+    operator.eq,
+    operator.ne,
+]
+
 
 @pytest.mark.parametrize(
     "data",
@@ -1442,3 +1451,20 @@ def test_timdelta_binop_tz_timestamp(op):
 def test_timedelta_getitem_na():
     s = cudf.Series([1, 2, None, 3], dtype="timedelta64[ns]")
     assert s[2] is cudf.NaT
+
+
+@pytest.mark.parametrize("data1", [[123, 456, None, 321, None]])
+@pytest.mark.parametrize("data2", [[123, 456, 789, None, None]])
+@pytest.mark.parametrize("op", _cmpops)
+def test_timedelta_series_cmpops_pandas_compatibility(data1, data2, op):
+    gsr1 = cudf.Series(data=data1, dtype="timedelta64[ns]")
+    psr1 = gsr1.to_pandas()
+
+    gsr2 = cudf.Series(data=data2, dtype="timedelta64[ns]")
+    psr2 = gsr2.to_pandas()
+
+    expect = op(psr1, psr2)
+    with cudf.option_context("mode.pandas_compatible", True):
+        got = op(gsr1, gsr2)
+
+    assert_eq(expect, got)