diff --git a/Doc/library/asyncio-task.rst b/Doc/library/asyncio-task.rst
index 1a13ad387f89b22..6df87d4d71a3657 100644
--- a/Doc/library/asyncio-task.rst
+++ b/Doc/library/asyncio-task.rst
@@ -175,6 +175,9 @@ other coroutines::
    * a *coroutine object*: an object returned by calling a
      *coroutine function*.
 
+   Generator-based coroutines, created with :func:`types.coroutine`, are
+   covered by neither term and are not supported by asyncio.
+
 
 .. rubric:: Tasks
 
@@ -1220,6 +1223,10 @@ Introspection
 
    .. versionadded:: 3.4
 
+   .. versionchanged:: 3.12
+      Generator-based coroutines are no longer supported, and ``False``
+      is returned for them.
+
 .. _asyncio-task-obj:
 
 Task object