diff --git a/.travis.yml b/.travis.yml
index 46a7364be..a37a055bd 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -31,6 +31,8 @@ jobs:
       env: DJANGO="Django==2.1.*"
     - python: "3.7"
       env: DJANGO="Django==2.2.*"
+    - python: "3.8"
+      env: DJANGO="Django==2.2.*"
 
     - stage: lint
       install: pip install -U -e .[tests] black pyflakes isort
diff --git a/channels/utils.py b/channels/utils.py
index d1813e1c3..19c0d482e 100644
--- a/channels/utils.py
+++ b/channels/utils.py
@@ -1,6 +1,5 @@
 import asyncio
 import types
-from concurrent.futures import CancelledError
 
 
 def name_that_thing(thing):
@@ -57,5 +56,5 @@ async def await_many_dispatch(consumer_callables, dispatch):
             task.cancel()
             try:
                 await task
-            except CancelledError:
+            except asyncio.CancelledError:
                 pass
diff --git a/setup.py b/setup.py
index 65db88137..c6d48aacc 100644
--- a/setup.py
+++ b/setup.py
@@ -14,7 +14,7 @@
     python_requires='>=3.5',
     install_requires=[
         'Django>=1.11',
-        'asgiref~=3.0',
+        'asgiref~=3.2',
         'daphne~=2.3',
     ],
     extras_require={
@@ -39,6 +39,7 @@
         'Programming Language :: Python :: 3.5',
         'Programming Language :: Python :: 3.6',
         'Programming Language :: Python :: 3.7',
+        'Programming Language :: Python :: 3.8',
         'Topic :: Internet :: WWW/HTTP',
     ],
 )
diff --git a/tests/test_testing.py b/tests/test_testing.py
index 0d8c5c7b0..a67cca383 100644
--- a/tests/test_testing.py
+++ b/tests/test_testing.py
@@ -1,4 +1,4 @@
-from concurrent.futures import TimeoutError
+import asyncio
 from urllib.parse import unquote
 
 import pytest
@@ -121,7 +121,7 @@ async def test_timeout_disconnect():
     assert subprotocol is None
     # Test sending text (will error internally)
     await communicator.send_to(text_data="hello")
-    with pytest.raises(TimeoutError):
+    with pytest.raises(asyncio.TimeoutError):
         await communicator.receive_from()
     # Close out
     await communicator.disconnect()
diff --git a/tox.ini b/tox.ini
index f24a61445..3dd39f4f9 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py{36,37}-dj{11,21,22,master}
+envlist = py{36,37,38}-dj{11,21,22,master}
 
 [testenv]
 usedevelop = true