diff --git a/awaitlet/base.py b/awaitlet/base.py
index 1accf9c..70eaebd 100644
--- a/awaitlet/base.py
+++ b/awaitlet/base.py
@@ -1,6 +1,6 @@
 from __future__ import annotations
 
-import asyncio
+import inspect
 import sys
 from typing import Any
 from typing import Awaitable
@@ -9,6 +9,7 @@
 from typing import TYPE_CHECKING
 from typing import TypeVar
 
+from anyio import get_cancelled_exc_class
 from greenlet import greenlet
 
 from .util.typing import TypeGuard
@@ -20,7 +21,7 @@ def is_exit_exception(e: BaseException) -> bool:
     # note asyncio.CancelledError is already BaseException
     # so was an exit exception in any case
     return not isinstance(e, Exception) or isinstance(
-        e, (asyncio.TimeoutError, asyncio.CancelledError)
+        e, (TimeoutError, get_cancelled_exc_class())
     )
 
 
@@ -50,7 +51,7 @@ def iscoroutine(
     ) -> TypeGuard[Coroutine[Any, Any, _T_co]]: ...
 
 else:
-    iscoroutine = asyncio.iscoroutine
+    iscoroutine = inspect.isawaitable
 
 
 def _safe_cancel_awaitable(awaitable: Awaitable[Any]) -> None:
diff --git a/pyproject.toml b/pyproject.toml
index 79c7ac9..4338bb7 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -25,6 +25,7 @@ classifiers = [
 ]
 
 dependencies = [
+    "anyio >= 4, < 5",
     "greenlet >= 1",
     "typing-extensions >= 4.6.0",
 ]
diff --git a/tests/test_concurrency.py b/tests/test_concurrency.py
index ab3862a..b792127 100644
--- a/tests/test_concurrency.py
+++ b/tests/test_concurrency.py
@@ -1,7 +1,7 @@
-import asyncio
 import contextvars
 import random
 
+import anyio
 from awaitlet import async_def
 from awaitlet import awaitlet
 from awaitlet import NoAwaitletContext
@@ -42,7 +42,7 @@ async def test_propagate_cancelled(self):
         cleanup = []
 
         async def async_meth_raise():
-            raise asyncio.CancelledError()
+            raise anyio.get_cancelled_exc_class()
 
         def sync_meth():
             try:
@@ -54,7 +54,7 @@ def sync_meth():
         async def run_w_cancel():
             await async_def(sync_meth)
 
-        with expect_raises(asyncio.CancelledError, check_context=False):
+        with expect_raises(anyio.get_cancelled_exc_class(), check_context=False):
             await run_w_cancel()
 
         assert cleanup
@@ -112,12 +112,12 @@ async def test_contextvars(self):
         # NOTE: sleep here is not necessary. It's used to simulate IO
         # ensuring that task are not run sequentially
         async def async_inner(val):
-            await asyncio.sleep(random.uniform(0.005, 0.015))
+            await anyio.sleep(random.uniform(0.005, 0.015))
             eq_(val, var.get())
             return var.get()
 
         async def async_set(val):
-            await asyncio.sleep(random.uniform(0.005, 0.015))
+            await anyio.sleep(random.uniform(0.005, 0.015))
             var.set(val)
 
         def inner(val):
@@ -140,18 +140,17 @@ def inner(val):
 
             return retval
 
+        values = set()
+
         async def task(val):
-            await asyncio.sleep(random.uniform(0.005, 0.015))
+            await anyio.sleep(random.uniform(0.005, 0.015))
             var.set(val)
-            await asyncio.sleep(random.uniform(0.005, 0.015))
-            return await async_def(inner, val)
-
-        values = {
-            await coro
-            for coro in asyncio.as_completed(
-                [task(i) for i in range(concurrency)]
-            )
-        }
+            await anyio.sleep(random.uniform(0.005, 0.015))
+            values.add(await async_def(inner, val))
+
+        async with anyio.create_task_group() as tg:
+            for i in range(concurrency):
+                tg.start_soon(task, i)
         eq_(values, set(range(concurrency * 2, concurrency * 3)))
 
     @async_test