diff --git a/Doc/library/asyncio-eventloop.rst b/Doc/library/asyncio-eventloop.rst
index 8f7974b..2fd4cf3 100644
--- a/Doc/library/asyncio-eventloop.rst
+++ b/Doc/library/asyncio-eventloop.rst
@@ -167,6 +167,18 @@
 
    .. versionadded:: 3.6
 
+.. coroutinemethod:: loop.shutdown_default_executor()
+
+   Schedule the closure of the default executor and wait for it to join all of
+   the threads in the :class:`ThreadPoolExecutor`. After calling this method, a
+   :exc:`RuntimeError` will be raised if :meth:`loop.run_in_executor` is called
+   while using the default executor.
+
+   Note that there is no need to call this function when
+   :func:`asyncio.run` is used.
+
+   .. versionadded:: 3.9
+
 
 Scheduling callbacks
 ^^^^^^^^^^^^^^^^^^^^
diff --git a/Doc/library/asyncio-task.rst b/Doc/library/asyncio-task.rst
index 57e0e07..d932042 100644
--- a/Doc/library/asyncio-task.rst
+++ b/Doc/library/asyncio-task.rst
@@ -213,8 +213,8 @@
 .. function:: run(coro, \*, debug=False)
 
     This function runs the passed coroutine, taking care of
-    managing the asyncio event loop and *finalizing asynchronous
-    generators*.
+    managing the asyncio event loop, *finalizing asynchronous
+    generators*, and closing the threadpool.
 
     This function cannot be called when another asyncio event loop is
     running in the same thread.
@@ -229,6 +229,8 @@
        **Important:** this function has been added to asyncio in
        Python 3.7 on a :term:`provisional basis <provisional api>`.
 
+    .. versionchanged:: 3.9
+       Updated to use :meth:`loop.shutdown_default_executor`.
 
 Creating Tasks
 ==============