diff --git a/tenacity/retry.py b/tenacity/retry.py
index df0cc4d6..60c4b626 100644
--- a/tenacity/retry.py
+++ b/tenacity/retry.py
@@ -126,7 +126,7 @@ def __init__(
         super().__init__(self._check)
 
     def _check(self, e: BaseException) -> bool:
-        return not isinstance(e, self.exception_types)
+        return isinstance(e, Exception) and not isinstance(e, self.exception_types)
 
 
 class retry_unless_exception_type(retry_if_exception):
diff --git a/tests/test_asyncio.py b/tests/test_asyncio.py
index 7b5c6416..e8b3a942 100644
--- a/tests/test_asyncio.py
+++ b/tests/test_asyncio.py
@@ -159,6 +159,28 @@ def after(retry_state: RetryCallState) -> None:
         assert len(set(things)) == 1
         assert list(attempt_nos2) == [1, 2, 3]
 
+    @asynctest
+    async def test_retry_if_not_exception_type_does_not_swallow_cancelled_error(
+        self,
+    ) -> None:
+        attempts = 0
+
+        @retry(
+            retry=tenacity.retry_if_not_exception_type(ValueError),
+            stop=stop_after_attempt(2),
+            wait=wait_fixed(0),
+            reraise=True,
+        )
+        async def always_sleep() -> None:
+            nonlocal attempts
+            attempts += 1
+            await asyncio.sleep(1)
+
+        with pytest.raises(asyncio.TimeoutError):
+            await asyncio.wait_for(always_sleep(), 0.01)
+
+        assert attempts == 1
+
 
 class TestAsyncEnabled(unittest.TestCase):
     @asynctest
diff --git a/tests/test_tenacity.py b/tests/test_tenacity.py
index 6a397392..63ec7c3a 100644
--- a/tests/test_tenacity.py
+++ b/tests/test_tenacity.py
@@ -1265,6 +1265,27 @@ def test_retry_except_exception_of_type(self) -> None:
             self.assertTrue(isinstance(err, IOError))
             print(err)
 
+    def test_retry_except_exception_of_type_does_not_retry_base_exception(self) -> None:
+        calls = 0
+
+        class CustomBaseError(BaseException):
+            pass
+
+        @retry(
+            stop=tenacity.stop_after_attempt(3),
+            retry=tenacity.retry_if_not_exception_type(IOError),
+            reraise=True,
+        )
+        def raises_base_exception() -> None:
+            nonlocal calls
+            calls += 1
+            raise CustomBaseError
+
+        with pytest.raises(CustomBaseError):
+            raises_base_exception()
+
+        assert calls == 1
+
     def test_retry_until_exception_of_type_attempt_number(self) -> None:
         try:
             self.assertTrue(