diff --git a/conda-environment.yml b/conda-environment.yml
index 6d31dce548..fed33d57a8 100644
--- a/conda-environment.yml
+++ b/conda-environment.yml
@@ -3,7 +3,7 @@ channels:
   - conda-forge
 dependencies:
   - ansimarkup >=1.0.0
-  - async-timeout>=3.0.0
+  - async-timeout>=3.0.0 # [py<3.11]
   - colorama >=0.4,<1.0
   - graphene >=2.1,<3
   - graphviz  # for static graphing
diff --git a/cylc/flow/network/ssh_client.py b/cylc/flow/network/ssh_client.py
index d2ed0dd33e..a68a16876b 100644
--- a/cylc/flow/network/ssh_client.py
+++ b/cylc/flow/network/ssh_client.py
@@ -14,17 +14,36 @@
 # You should have received a copy of the GNU General Public License
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
-from async_timeout import timeout as asyncto
 import asyncio
 import json
 import os
-from typing import Any, List, Optional, Tuple, Union, Dict
+import sys
+from typing import (
+    Any,
+    Dict,
+    List,
+    Optional,
+    Tuple,
+    Union,
+)
 
-from cylc.flow.exceptions import ClientError, ClientTimeout
+from cylc.flow.exceptions import (
+    ClientError,
+    ClientTimeout,
+)
 from cylc.flow.network.client import WorkflowRuntimeClientBase
 from cylc.flow.network.client_factory import CommsMeth
 from cylc.flow.remote import remote_cylc_cmd
-from cylc.flow.workflow_files import load_contact_file, ContactFileFields
+from cylc.flow.workflow_files import (
+    ContactFileFields,
+    load_contact_file,
+)
+
+
+if sys.version_info[:2] >= (3, 11):
+    from asyncio import timeout as asyncto
+else:
+    from async_timeout import timeout as asyncto
 
 
 class WorkflowRuntimeClient(WorkflowRuntimeClientBase):
diff --git a/setup.cfg b/setup.cfg
index 3dfba8e9a7..abdf10fd75 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -63,7 +63,7 @@ include_package_data = True
 python_requires = >=3.7
 install_requires =
     ansimarkup>=1.0.0
-    async-timeout>=3.0.0
+    async-timeout>=3.0.0; python_version < "3.11"
     colorama>=0.4,<1
     graphene>=2.1,<3
     # Note: can't pin jinja2 any higher than this until we give up on Cylc 7 back-compat
diff --git a/tests/integration/test_publisher.py b/tests/integration/test_publisher.py
index c1fe7e1bcd..4e7d00cd52 100644
--- a/tests/integration/test_publisher.py
+++ b/tests/integration/test_publisher.py
@@ -13,15 +13,20 @@
 #
 # You should have received a copy of the GNU General Public License
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
-from async_timeout import timeout
-import pytest
+import sys
 
 from cylc.flow.network.subscriber import (
     WorkflowSubscriber,
-    process_delta_msg
+    process_delta_msg,
 )
 
 
+if sys.version_info[:2] >= (3, 11):
+    from asyncio import timeout
+else:
+    from async_timeout import timeout
+
+
 async def test_publisher(flow, scheduler, run, one_conf, port_range):
     """It should publish deltas when the flow starts."""
     id_ = flow(one_conf)
diff --git a/tests/integration/test_replier.py b/tests/integration/test_replier.py
index ce0b53fdaa..3f7334eca9 100644
--- a/tests/integration/test_replier.py
+++ b/tests/integration/test_replier.py
@@ -14,13 +14,18 @@
 # You should have received a copy of the GNU General Public License
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
-from async_timeout import timeout
+import sys
 from cylc.flow.network import decode_
 from cylc.flow.network.client import WorkflowRuntimeClient
 import asyncio
 
 import pytest
 
+if sys.version_info[:2] >= (3, 11):
+    from asyncio import timeout
+else:
+    from async_timeout import timeout
+
 
 async def test_listener(one, start, ):
     """Test listener."""
diff --git a/tests/integration/test_server.py b/tests/integration/test_server.py
index bc7103b836..b8c46b1a2c 100644
--- a/tests/integration/test_server.py
+++ b/tests/integration/test_server.py
@@ -14,9 +14,9 @@
 # You should have received a copy of the GNU General Public License
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
-from typing import Callable
-from async_timeout import timeout
 from getpass import getuser
+import sys
+from typing import Callable
 
 import pytest
 
@@ -24,6 +24,12 @@
 from cylc.flow.scheduler import Scheduler
 
 
+if sys.version_info[:2] >= (3, 11):
+    from asyncio import timeout
+else:
+    from async_timeout import timeout
+
+
 @pytest.fixture(scope='module')
 async def myflow(mod_flow, mod_scheduler, mod_run, mod_one_conf):
     id_ = mod_flow(mod_one_conf)
diff --git a/tests/integration/test_workflow_events.py b/tests/integration/test_workflow_events.py
index b41b03e721..c086ca6475 100644
--- a/tests/integration/test_workflow_events.py
+++ b/tests/integration/test_workflow_events.py
@@ -15,13 +15,19 @@
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
 import asyncio
+import sys
 
-from async_timeout import timeout as async_timeout
 import pytest
 
 from cylc.flow.scheduler import SchedulerError
 
 
+if sys.version_info[:2] >= (3, 11):
+    from asyncio import timeout as async_timeout
+else:
+    from async_timeout import timeout as async_timeout
+
+
 EVENTS = (
     'startup',
     'shutdown',
diff --git a/tests/integration/tui/test_updater.py b/tests/integration/tui/test_updater.py
index 3fa310b696..0077fa6204 100644
--- a/tests/integration/tui/test_updater.py
+++ b/tests/integration/tui/test_updater.py
@@ -19,9 +19,9 @@
 from pathlib import Path
 from queue import Queue
 import re
+import sys
 from time import time
 
-from async_timeout import timeout
 import pytest
 
 from cylc.flow.cycling.integer import IntegerPoint
@@ -33,6 +33,12 @@
 from cylc.flow.workflow_status import WorkflowStatus
 
 
+if sys.version_info[:2] >= (3, 11):
+    from asyncio import timeout
+else:
+    from async_timeout import timeout
+
+
 @pytest.fixture
 def updater(monkeypatch, test_dir):
     """Return an updater ready for testing."""
diff --git a/tests/integration/utils/flow_tools.py b/tests/integration/utils/flow_tools.py
index ba5e3d0470..7a341e8515 100644
--- a/tests/integration/utils/flow_tools.py
+++ b/tests/integration/utils/flow_tools.py
@@ -22,23 +22,40 @@
 """
 
 import asyncio
-from pathlib import Path
-from async_timeout import timeout
-from contextlib import asynccontextmanager, contextmanager
+from contextlib import (
+    asynccontextmanager,
+    contextmanager,
+)
 import logging
-import pytest
-from typing import Any, Optional, Union
+from pathlib import Path
 from secrets import token_hex
+import sys
+from typing import (
+    Any,
+    Optional,
+    Union,
+)
+
+import pytest
 
 from cylc.flow import CYLC_LOG
-from cylc.flow.workflow_files import WorkflowFiles
-from cylc.flow.scheduler import Scheduler, SchedulerStop
+from cylc.flow.scheduler import (
+    Scheduler,
+    SchedulerStop,
+)
 from cylc.flow.scheduler_cli import RunOptions
+from cylc.flow.workflow_files import WorkflowFiles
 from cylc.flow.workflow_status import StopMode
 
 from .flow_writer import flow_config_str
 
 
+if sys.version_info[:2] >= (3, 11):
+    from asyncio import timeout
+else:
+    from async_timeout import timeout
+
+
 def _make_src_flow(src_path, conf, filename=WorkflowFiles.FLOW_FILE):
     """Construct a workflow on the filesystem"""
     flow_src_dir = (src_path / token_hex(4))