diff --git a/Lib/test/test_asyncio/functional.py b/Lib/test/test_asyncio/functional.py
index 74490a869de9d9..d19c7a612ccf86 100644
--- a/Lib/test/test_asyncio/functional.py
+++ b/Lib/test/test_asyncio/functional.py
@@ -29,10 +29,6 @@ def setUp(self):
         self.loop.set_exception_handler(self.loop_exception_handler)
         self.__unhandled_exceptions = []
 
-        # Disable `_get_running_loop`.
-        self._old_get_running_loop = asyncio.events._get_running_loop
-        asyncio.events._get_running_loop = lambda: None
-
     def tearDown(self):
         try:
             self.loop.close()
@@ -43,7 +39,6 @@ def tearDown(self):
                 self.fail('unexpected calls to loop.call_exception_handler()')
 
         finally:
-            asyncio.events._get_running_loop = self._old_get_running_loop
             asyncio.set_event_loop(None)
             self.loop = None
 
diff --git a/Lib/test/test_asyncio/test_futures.py b/Lib/test/test_asyncio/test_futures.py
index fe3d44227c83cc..42b9499edd78bd 100644
--- a/Lib/test/test_asyncio/test_futures.py
+++ b/Lib/test/test_asyncio/test_futures.py
@@ -918,6 +918,8 @@ def _get_future_cls(self):
         return futures._PyFuture
 
 
+@unittest.skipUnless(hasattr(futures, '_CFuture'),
+                     'requires the C _asyncio module')
 class CFutureInheritanceTests(BaseFutureInheritanceTests,
                               test_utils.TestCase):
     def _get_future_cls(self):
diff --git a/Lib/test/test_asyncio/test_sslproto.py b/Lib/test/test_asyncio/test_sslproto.py
index e87863eb712373..a47e43dd4cadb4 100644
--- a/Lib/test/test_asyncio/test_sslproto.py
+++ b/Lib/test/test_asyncio/test_sslproto.py
@@ -278,6 +278,7 @@ async def client(addr):
 
         # No garbage is left if SSL is closed uncleanly
         client_context = weakref.ref(client_context)
+        support.gc_collect()
         self.assertIsNone(client_context())
 
     def test_create_connection_memory_leak(self):
@@ -341,6 +342,7 @@ async def client(addr):
         # No garbage is left for SSL client from loop.create_connection, even
         # if user stores the SSLTransport in corresponding protocol instance
         client_context = weakref.ref(client_context)
+        support.gc_collect()
         self.assertIsNone(client_context())
 
     def test_start_tls_client_buf_proto_1(self):
@@ -640,6 +642,7 @@ async def client(addr):
         # The 10s handshake timeout should be cancelled to free related
         # objects without really waiting for 10s
         client_sslctx = weakref.ref(client_sslctx)
+        support.gc_collect()
         self.assertIsNone(client_sslctx())
 
     def test_create_connection_ssl_slow_handshake(self):
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index 86710872ace024..de003737f906ef 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -2875,15 +2875,18 @@ class GenericTaskTests(test_utils.TestCase):
     def test_future_subclass(self):
         self.assertTrue(issubclass(asyncio.Task, asyncio.Future))
 
+    @support.cpython_only
     def test_asyncio_module_compiled(self):
         # Because of circular imports it's easy to make _asyncio
         # module non-importable.  This is a simple test that will
         # fail on systems where C modules were successfully compiled
-        # (hence the test for _functools), but _asyncio somehow didn't.
+        # (hence the test for _functools etc), but _asyncio somehow didn't.
         try:
             import _functools
+            import _json
+            import _pickle
         except ImportError:
-            pass
+            self.skipTest('C modules are not available')
         else:
             try:
                 import _asyncio
diff --git a/Misc/NEWS.d/next/Tests/2021-08-26-14-20-44.bpo-45011.mQZdXU.rst b/Misc/NEWS.d/next/Tests/2021-08-26-14-20-44.bpo-45011.mQZdXU.rst
new file mode 100644
index 00000000000000..64e701e2f29f49
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2021-08-26-14-20-44.bpo-45011.mQZdXU.rst
@@ -0,0 +1,3 @@
+Made tests relying on the :mod:`_asyncio` C extension module optional to
+allow running on alternative Python implementations. Patch by Serhiy
+Storchaka.