diff --git a/CHANGES/6757.misc b/CHANGES/6757.misc
new file mode 100644
index 00000000000..986e3feb95f
--- /dev/null
+++ b/CHANGES/6757.misc
@@ -0,0 +1,3 @@
+Work around the changes in 3.11, e.g. :py:class:`~asyncio.TimeoutError` is an :py:class:`OSError`,
+and :py:class:`~unittest.IsolatedAsyncioTestCase` calls :py:function:`~asyncio.set_event_loop`
+differently -- by :user:`graingert`.
diff --git a/aiohttp/client.py b/aiohttp/client.py
index d05689ca6b7..a97190d078a 100644
--- a/aiohttp/client.py
+++ b/aiohttp/client.py
@@ -532,6 +532,8 @@ async def _request(
                     except ClientError:
                         raise
                     except OSError as exc:
+                        if exc.errno is None and isinstance(exc, asyncio.TimeoutError):
+                            raise
                         raise ClientOSError(*exc.args) from exc
 
                     self._cookie_jar.update_cookies(resp.cookies, resp.url)
diff --git a/aiohttp/client_reqrep.py b/aiohttp/client_reqrep.py
index 733cd48f63c..9478e8d36c5 100644
--- a/aiohttp/client_reqrep.py
+++ b/aiohttp/client_reqrep.py
@@ -537,12 +537,15 @@ async def write_bytes(
 
             await writer.write_eof()
         except OSError as exc:
-            new_exc = ClientOSError(
-                exc.errno, "Can not write request body for %s" % self.url
-            )
-            new_exc.__context__ = exc
-            new_exc.__cause__ = exc
-            protocol.set_exception(new_exc)
+            if exc.errno is None and isinstance(exc, asyncio.TimeoutError):
+                protocol.set_exception(exc)
+            else:
+                new_exc = ClientOSError(
+                    exc.errno, "Can not write request body for %s" % self.url
+                )
+                new_exc.__context__ = exc
+                new_exc.__cause__ = exc
+                protocol.set_exception(new_exc)
         except asyncio.CancelledError as exc:
             if not conn.closed:
                 protocol.set_exception(exc)
diff --git a/aiohttp/connector.py b/aiohttp/connector.py
index 86399b84272..7dbbf4f2d80 100644
--- a/aiohttp/connector.py
+++ b/aiohttp/connector.py
@@ -970,6 +970,8 @@ async def _wrap_create_connection(
         except ssl_errors as exc:
             raise ClientConnectorSSLError(req.connection_key, exc) from exc
         except OSError as exc:
+            if exc.errno is None and isinstance(exc, asyncio.TimeoutError):
+                raise
             raise client_error(req.connection_key, exc) from exc
 
     def _warn_about_tls_in_tls(
@@ -1049,6 +1051,8 @@ async def _start_tls_connection(
         except ssl_errors as exc:
             raise ClientConnectorSSLError(req.connection_key, exc) from exc
         except OSError as exc:
+            if exc.errno is None and isinstance(exc, asyncio.TimeoutError):
+                raise
             raise client_error(req.connection_key, exc) from exc
         except TypeError as type_err:
             # Example cause looks like this:
@@ -1100,6 +1104,8 @@ def drop_exception(fut: "asyncio.Future[List[Dict[str, Any]]]") -> None:
             host_resolved.add_done_callback(drop_exception)
             raise
         except OSError as exc:
+            if exc.errno is None and isinstance(exc, asyncio.TimeoutError):
+                raise
             # in case of proxy it is not ClientProxyConnectionError
             # it is problem of resolving proxy ip itself
             raise ClientConnectorError(req.connection_key, exc) from exc
@@ -1293,6 +1299,8 @@ async def _create_connection(
                     self._factory, self._path
                 )
         except OSError as exc:
+            if exc.errno is None and isinstance(exc, asyncio.TimeoutError):
+                raise
             raise UnixClientConnectorError(self.path, req.connection_key, exc) from exc
 
         return cast(ResponseHandler, proto)
@@ -1358,6 +1366,8 @@ async def _create_connection(
                 # other option is to manually set transport like
                 # `proto.transport = trans`
         except OSError as exc:
+            if exc.errno is None and isinstance(exc, asyncio.TimeoutError):
+                raise
             raise ClientConnectorError(req.connection_key, exc) from exc
 
         return cast(ResponseHandler, proto)
diff --git a/aiohttp/test_utils.py b/aiohttp/test_utils.py
index 82956986b9d..e0aacbb68fc 100644
--- a/aiohttp/test_utils.py
+++ b/aiohttp/test_utils.py
@@ -430,12 +430,12 @@ def get_app(self) -> Application:
         raise RuntimeError("Did you forget to define get_application()?")
 
     def setUp(self) -> None:
-        try:
-            self.loop = asyncio.get_running_loop()
-        except RuntimeError:
-            self.loop = asyncio.get_event_loop_policy().get_event_loop()
+        if not PY_38:
+            asyncio.get_event_loop().run_until_complete(self.asyncSetUp())
 
-        self.loop.run_until_complete(self.setUpAsync())
+    async def asyncSetUp(self) -> None:
+        self.loop = asyncio.get_running_loop()
+        return await self.setUpAsync()
 
     async def setUpAsync(self) -> None:
         self.app = await self.get_application()
@@ -445,7 +445,11 @@ async def setUpAsync(self) -> None:
         await self.client.start_server()
 
     def tearDown(self) -> None:
-        self.loop.run_until_complete(self.tearDownAsync())
+        if not PY_38:
+            self.loop.run_until_complete(self.asyncTearDown())
+
+    async def asyncTearDown(self) -> None:
+        return await self.tearDownAsync()
 
     async def tearDownAsync(self) -> None:
         await self.client.close()