diff --git a/Doc/library/asyncio-task.rst b/Doc/library/asyncio-task.rst
index 42e2b4e..bc8a272 100644
--- a/Doc/library/asyncio-task.rst
+++ b/Doc/library/asyncio-task.rst
@@ -453,7 +453,8 @@
    wrap it in :func:`shield`.
 
    The function will wait until the future is actually cancelled,
-   so the total wait time may exceed the *timeout*.
+   so the total wait time may exceed the *timeout*. If an exception
+   happens during cancellation, it is propagated.
 
    If the wait is cancelled, the future *aw* is also cancelled.
 
diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index 717837d..f5de1a2 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -496,7 +496,15 @@
             # after wait_for() returns.
             # See https://bugs.python.org/issue32751
             await _cancel_and_wait(fut, loop=loop)
-            raise exceptions.TimeoutError()
+            # In case task cancellation failed with some
+            # exception, we should re-raise it
+            # See https://bugs.python.org/issue40607
+            try:
+                fut.result()
+            except exceptions.CancelledError as exc:
+                raise exceptions.TimeoutError() from exc
+            else:
+                raise exceptions.TimeoutError()
     finally:
         timeout_handle.cancel()
 
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index 6eb6b46..0f8d921 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -80,6 +80,12 @@
         return self
 
 
+# The following value can be used as a very small timeout:
+# it passes check "timeout > 0", but has almost
+# no effect on the test performance
+_EPSILON = 0.0001
+
+
 class BaseTaskTests:
 
     Task = None
@@ -904,12 +910,53 @@
 
             inner_task = self.new_task(loop, inner())
 
-            with self.assertRaises(asyncio.TimeoutError):
-                await asyncio.wait_for(inner_task, timeout=0.1)
+            await asyncio.wait_for(inner_task, timeout=_EPSILON)
 
-            self.assertTrue(task_done)
+        with self.assertRaises(asyncio.TimeoutError) as cm:
+            loop.run_until_complete(foo())
 
-        loop.run_until_complete(foo())
+        self.assertTrue(task_done)
+        chained = cm.exception.__context__
+        self.assertEqual(type(chained), asyncio.CancelledError)
+
+    def test_wait_for_reraises_exception_during_cancellation(self):
+        loop = asyncio.new_event_loop()
+        self.addCleanup(loop.close)
+
+        class FooException(Exception):
+            pass
+
+        async def foo():
+            async def inner():
+                try:
+                    await asyncio.sleep(0.2)
+                finally:
+                    raise FooException
+
+            inner_task = self.new_task(loop, inner())
+
+            await asyncio.wait_for(inner_task, timeout=_EPSILON)
+
+        with self.assertRaises(FooException):
+            loop.run_until_complete(foo())
+
+    def test_wait_for_raises_timeout_error_if_returned_during_cancellation(self):
+        loop = asyncio.new_event_loop()
+        self.addCleanup(loop.close)
+
+        async def foo():
+            async def inner():
+                try:
+                    await asyncio.sleep(0.2)
+                except asyncio.CancelledError:
+                    return 42
+
+            inner_task = self.new_task(loop, inner())
+
+            await asyncio.wait_for(inner_task, timeout=_EPSILON)
+
+        with self.assertRaises(asyncio.TimeoutError):
+            loop.run_until_complete(foo())
 
     def test_wait_for_self_cancellation(self):
         loop = asyncio.new_event_loop()
diff --git a/Misc/ACKS b/Misc/ACKS
index b479aa5..fad920b 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -1593,6 +1593,7 @@
 Ngalim Siregar
 Kragen Sitaker
 Kaartic Sivaraam
+Roman Skurikhin
 Ville Skyttä
 Michael Sloan
 Nick Sloan
diff --git a/Misc/NEWS.d/next/Library/2020-05-13-15-32-13.bpo-40607.uSPFCi.rst b/Misc/NEWS.d/next/Library/2020-05-13-15-32-13.bpo-40607.uSPFCi.rst
new file mode 100644
index 0000000..8060628
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-05-13-15-32-13.bpo-40607.uSPFCi.rst
@@ -0,0 +1,3 @@
+When cancelling a task due to timeout, :meth:`asyncio.wait_for` will now
+propagate the exception if an error happens during cancellation.
+Patch by Roman Skurikhin.