diff --git a/pandas-stubs/core/series.pyi b/pandas-stubs/core/series.pyi
index b017b6840..91923f9eb 100644
--- a/pandas-stubs/core/series.pyi
+++ b/pandas-stubs/core/series.pyi
@@ -61,7 +61,10 @@ from pandas.core.window.rolling import (
     Rolling,
     Window,
 )
-from typing_extensions import TypeAlias
+from typing_extensions import (
+    Never,
+    TypeAlias,
+)
 import xarray as xr
 
 from pandas._libs.missing import NAType
@@ -1211,7 +1214,7 @@ class Series(IndexOpsMixin, NDFrame, Generic[S1]):
     def __add__(self, other: Timestamp) -> TimestampSeries: ...
     @overload
     def __add__(
-        self, other: num | _str | Timedelta | _ListLike | Series[S1]
+        self, other: num | _str | Timedelta | _ListLike | Series[S1] | np.timedelta64
     ) -> Series: ...
     # ignore needed for mypy as we want different results based on the arguments
     @overload
@@ -1243,7 +1246,9 @@ class Series(IndexOpsMixin, NDFrame, Generic[S1]):
     def __le__(self, other: S1 | _ListLike | Series[S1]) -> Series[_bool]: ...
     def __lt__(self, other: S1 | _ListLike | Series[S1]) -> Series[_bool]: ...
     @overload
-    def __mul__(self, other: Timedelta | TimedeltaSeries) -> TimedeltaSeries: ...
+    def __mul__(
+        self, other: Timedelta | TimedeltaSeries | np.timedelta64
+    ) -> TimedeltaSeries: ...
     @overload
     def __mul__(self, other: num | _ListLike | Series) -> Series: ...
     def __mod__(self, other: num | _ListLike | Series[S1]) -> Series[S1]: ...
@@ -1304,17 +1309,19 @@ class Series(IndexOpsMixin, NDFrame, Generic[S1]):
     ) -> TimedeltaSeries: ...
     @overload
     def __sub__(
-        self: Series[Timestamp], other: Timedelta | TimedeltaSeries | TimedeltaIndex
+        self: Series[Timestamp],
+        other: Timedelta | TimedeltaSeries | TimedeltaIndex | np.timedelta64,
     ) -> TimestampSeries: ...
     @overload
     def __sub__(
-        self: Series[Timedelta], other: Timedelta | TimedeltaSeries | TimedeltaIndex
+        self: Series[Timedelta],
+        other: Timedelta | TimedeltaSeries | TimedeltaIndex | np.timedelta64,
     ) -> TimedeltaSeries: ...
     @overload
     def __sub__(self, other: num | _ListLike | Series) -> Series: ...
     @overload
     def __truediv__(
-        self, other: Timedelta | TimedeltaSeries | TimedeltaIndex
+        self, other: Timedelta | TimedeltaSeries | TimedeltaIndex | np.timedelta64
     ) -> Series[float]: ...
     @overload
     def __truediv__(self, other: num | _ListLike | Series[S1]) -> Series: ...
@@ -1739,6 +1746,14 @@ class TimestampSeries(Series[Timestamp]):
     # ignore needed because of mypy
     @property
     def dt(self) -> TimestampProperties: ...  # type: ignore[override]
+    @overload  # type: ignore[override]
+    def __add__(
+        self, other: TimedeltaSeries | np.timedelta64 | TimestampSeries
+    ) -> TimestampSeries: ...
+    @overload
+    def __add__(self, other: Timestamp) -> Never: ...
+    def __mul__(self, other: TimestampSeries | np.timedelta64 | TimedeltaSeries) -> Never: ...  # type: ignore[override]
+    def __truediv__(self, other: TimestampSeries | np.timedelta64 | TimedeltaSeries) -> Never: ...  # type: ignore[override]
 
 class TimedeltaSeries(Series[Timedelta]):
     # ignores needed because of mypy
@@ -1747,12 +1762,18 @@ class TimedeltaSeries(Series[Timedelta]):
     @overload
     def __add__(self, other: Timestamp | DatetimeIndex) -> TimestampSeries: ...
     @overload
-    def __add__(self, other: Timedelta) -> TimedeltaSeries: ...
+    def __add__(self, other: Timedelta | np.timedelta64) -> TimedeltaSeries: ...
     def __radd__(self, pther: Timestamp | TimestampSeries) -> TimestampSeries: ...  # type: ignore[override]
-    def __mul__(self, other: num) -> TimedeltaSeries: ...  # type: ignore[override]
+    @overload  # type: ignore[override]
+    def __mul__(
+        self, other: TimestampSeries | np.timedelta64 | Timedelta | TimedeltaSeries
+    ) -> Never: ...
+    @overload
+    def __mul__(self, other: num) -> TimedeltaSeries: ...
     def __sub__(  # type: ignore[override]
-        self, other: Timedelta | TimedeltaSeries | TimedeltaIndex
+        self, other: Timedelta | TimedeltaSeries | TimedeltaIndex | np.timedelta64
     ) -> TimedeltaSeries: ...
+    def __truediv__(self, other: TimedeltaSeries | np.timedelta64 | TimedeltaIndex) -> Series[float]: ...  # type: ignore[override]
     @property
     def dt(self) -> TimedeltaProperties: ...  # type: ignore[override]
 
diff --git a/tests/test_timefuncs.py b/tests/test_timefuncs.py
index 62eebf6a4..b97369466 100644
--- a/tests/test_timefuncs.py
+++ b/tests/test_timefuncs.py
@@ -14,7 +14,10 @@
 import pandas as pd
 from pandas.core.indexes.numeric import IntegerIndex
 import pytz
-from typing_extensions import assert_type
+from typing_extensions import (
+    Never,
+    assert_type,
+)
 
 from pandas._libs import NaTType
 from pandas._libs.tslibs import BaseOffset
@@ -260,7 +263,7 @@ def fail_on_adding_two_timestamps() -> None:
     if TYPE_CHECKING_INVALID_USAGE:
         ssum: pd.Series = s1 + s2  # TODO both: ignore[operator]
         ts = pd.Timestamp("2022-06-30")
-        tsum: pd.Series = s1 + ts  # TODO both: ignore[operator]
+        tsum: pd.Series = s1 + ts  # pyright: ignore
 
 
 def test_dtindex_tzinfo() -> None:
@@ -1035,3 +1038,19 @@ def test_timedelta_range() -> None:
 def test_dateoffset_freqstr() -> None:
     offset = DateOffset(minutes=10)
     check(assert_type(offset.freqstr, str), str)
+
+
+def test_timedelta64_and_arithmatic_operator() -> None:
+    s1 = pd.Series(data=pd.date_range("1/1/2020", "2/1/2020"))
+    s2 = pd.Series(data=pd.date_range("1/1/2021", "2/1/2021"))
+    s3 = s2 - s1
+    td = np.timedelta64(1, "M")
+    check(assert_type((s1 - td), "TimestampSeries"), pd.Series, pd.Timestamp)
+    check(assert_type((s1 + td), "TimestampSeries"), pd.Series, pd.Timestamp)
+    check(assert_type((s3 - td), "TimedeltaSeries"), pd.Series, pd.Timedelta)
+    check(assert_type((s3 + td), "TimedeltaSeries"), pd.Series, pd.Timedelta)
+    check(assert_type((s3 / td), "pd.Series[float]"), pd.Series, float)
+    if TYPE_CHECKING_INVALID_USAGE:
+        assert_type((s1 * td), Never)  # pyright: ignore
+        assert_type((s1 / td), Never)  # pyright: ignore
+        assert_type((s3 * td), Never)  # pyright: ignore