diff --git a/Doc/library/asyncio-eventloop.rst b/Doc/library/asyncio-eventloop.rst
index 6fe5aa1b201..46af81fa635 100644
--- a/Doc/library/asyncio-eventloop.rst
+++ b/Doc/library/asyncio-eventloop.rst
@@ -58,13 +58,11 @@ Run an event loop
 
 .. method:: BaseEventLoop.close()
 
-   Close the event loop. The loop should not be running.
+   Close the event loop. The loop must not be running.
 
    This clears the queues and shuts down the executor, but does not wait for
    the executor to finish.
 
-   The event loop must not be running.
-
    This is idempotent and irreversible. No other methods should be called after
    this one.
 
diff --git a/Doc/library/asyncio.rst b/Doc/library/asyncio.rst
index 9857c932fde..90a152bf9b6 100644
--- a/Doc/library/asyncio.rst
+++ b/Doc/library/asyncio.rst
@@ -39,7 +39,7 @@ Here is a more detailed list of the package contents:
   you absolutely, positively have to use a library that makes blocking
   I/O calls.
 
-Table of content:
+Table of contents:
 
 .. toctree::
    :maxdepth: 3
@@ -55,6 +55,6 @@ Table of content:
 
 .. seealso::
 
-   The :mod:`asyncio` module was designed in the :PEP:`3156`. For a
+   The :mod:`asyncio` module was designed in :PEP:`3156`. For a
    motivational primer on transports and protocols, see :PEP:`3153`.