diff --git a/async_timeout/__init__.py b/async_timeout/__init__.py
index 6222654..31a4aef 100644
--- a/async_timeout/__init__.py
+++ b/async_timeout/__init__.py
@@ -198,6 +198,9 @@ def _do_exit(self, exc_type: Type[BaseException]) -> None:
         return None
 
     def _on_timeout(self, task: "asyncio.Task[None]") -> None:
+        # See Issue #229 and PR #230 for details      
+        if task._fut_waiter and task._fut_waiter.cancelled():  # type: ignore[attr-defined]  # noqa: E501
+            return
         task.cancel()
         self._state = _State.TIMEOUT
 
diff --git a/tests/test_timeout.py b/tests/test_timeout.py
index e76c54c..131c94d 100644
--- a/tests/test_timeout.py
+++ b/tests/test_timeout.py
@@ -1,9 +1,10 @@
 import asyncio
+import sys
 import time
 
 import pytest
 
-from async_timeout import timeout, timeout_at
+from async_timeout import Timeout, timeout, timeout_at
 
 
 @pytest.mark.asyncio
@@ -344,3 +345,55 @@ async def test_deprecated_with() -> None:
     with pytest.warns(DeprecationWarning):
         with timeout(1):
             await asyncio.sleep(0)
+
+
+@pytest.mark.skipif(sys.version_info < (3, 7), reason="Not supported in 3.6")
+@pytest.mark.asyncio
+async def test_race_condition_cancel_before() -> None:
+    """Test race condition when cancelling before timeout.
+
+    If cancel happens immediately before the timeout, then
+    the timeout may overrule the cancellation, making it
+    impossible to cancel some tasks.
+    """
+
+    async def test_task(deadline: float, loop: asyncio.AbstractEventLoop) -> None:
+        # We need the internal Timeout class to specify the deadline (not delay).
+        # This is needed to create the precise timing to reproduce the race condition.
+        with Timeout(deadline, loop):
+            await asyncio.sleep(10)
+
+    loop = asyncio.get_running_loop()
+    deadline = loop.time() + 1
+    t = asyncio.create_task(test_task(deadline, loop))
+    loop.call_at(deadline, t.cancel)
+    await asyncio.sleep(1.1)
+    # If we get a TimeoutError, then the code is broken.
+    with pytest.raises(asyncio.CancelledError):
+        await t
+
+
+@pytest.mark.skipif(sys.version_info < (3, 7), reason="Not supported in 3.6")
+@pytest.mark.asyncio
+async def test_race_condition_cancel_after() -> None:
+    """Test race condition when cancelling after timeout.
+
+    Similarly to the previous test, if a cancel happens
+    immediately after the timeout (but before the __exit__),
+    then the explicit cancel can get overruled again.
+    """
+
+    async def test_task(deadline: float, loop: asyncio.AbstractEventLoop) -> None:
+        # We need the internal Timeout class to specify the deadline (not delay).
+        # This is needed to create the precise timing to reproduce the race condition.
+        with Timeout(deadline, loop):
+            await asyncio.sleep(10)
+
+    loop = asyncio.get_running_loop()
+    deadline = loop.time() + 1
+    t = asyncio.create_task(test_task(deadline, loop))
+    loop.call_at(deadline + 0.000001, t.cancel)
+    await asyncio.sleep(1.1)
+    # If we get a TimeoutError, then the code is broken.
+    with pytest.raises(asyncio.CancelledError):
+        await t