diff --git a/Doc/library/sched.rst b/Doc/library/sched.rst
index 455cc70..957bdd3 100644
--- a/Doc/library/sched.rst
+++ b/Doc/library/sched.rst
@@ -102,12 +102,15 @@
    Return true if the event queue is empty.
 
 
-.. method:: scheduler.run()
+.. method:: scheduler.run(blocking=True)
 
-   Run all scheduled events. This function will wait  (using the :func:`delayfunc`
+   Run all scheduled events. This method will wait  (using the :func:`delayfunc`
    function passed to the constructor) for the next event, then execute it and so
    on until there are no more scheduled events.
 
+   If *blocking* is False executes the scheduled events due to expire soonest
+   (if any) and then return.
+
    Either *action* or *delayfunc* can raise an exception.  In either case, the
    scheduler will maintain a consistent state and propagate the exception.  If an
    exception is raised by *action*, the event will not be attempted in future calls
@@ -118,6 +121,9 @@
    the calling code is responsible for canceling  events which are no longer
    pertinent.
 
+   .. versionadded:: 3.3
+      *blocking* parameter was added.
+
 .. attribute:: scheduler.queue
 
    Read-only attribute returning a list of upcoming events in the order they
diff --git a/Doc/whatsnew/3.3.rst b/Doc/whatsnew/3.3.rst
index 91d3f90..c52eaf1 100644
--- a/Doc/whatsnew/3.3.rst
+++ b/Doc/whatsnew/3.3.rst
@@ -662,6 +662,12 @@
 sched
 -----
 
+* :meth:`~sched.scheduler.run` now accepts a *blocking* parameter which when
+  set to False makes the method execute the scheduled events due to expire
+  soonest (if any) and then return immediately.
+  This is useful in case you want to use the :class:`~sched.scheduler` in
+  non-blocking applications.  (Contributed by Giampaolo Rodolà in :issue:`13449`)
+
 * :class:`~sched.scheduler` class can now be safely used in multi-threaded
   environments.  (Contributed by Josiah Carlson and Giampaolo Rodolà in
   :issue:`8684`)
diff --git a/Lib/sched.py b/Lib/sched.py
index 5c4a7b6..5292fcf 100644
--- a/Lib/sched.py
+++ b/Lib/sched.py
@@ -91,8 +91,10 @@
         with self._lock:
             return not self._queue
 
-    def run(self):
+    def run(self, blocking=True):
         """Execute events until the queue is empty.
+        If blocking is False executes the scheduled events due to
+        expire soonest (if any) and then return.
 
         When there is a positive delay until the first event, the
         delay function is called and the event is left in the queue;
@@ -123,6 +125,8 @@
                 time, priority, action, argument, kwargs = checked_event = q[0]
                 now = timefunc()
                 if now < time:
+                    if not blocking:
+                        return
                     delayfunc(time - now)
                 else:
                     event = pop(q)
diff --git a/Lib/test/test_sched.py b/Lib/test/test_sched.py
index f5e159d..ae82f94 100644
--- a/Lib/test/test_sched.py
+++ b/Lib/test/test_sched.py
@@ -86,6 +86,16 @@
         scheduler.run()
         self.assertEqual(flag, [None])
 
+    def test_run_non_blocking(self):
+        l = []
+        fun = lambda x: l.append(x)
+        scheduler = sched.scheduler(time.time, time.sleep)
+        for x in [10, 9, 8, 7, 6]:
+            scheduler.enter(x, 1, fun, (x,))
+        scheduler.run(blocking=False)
+        self.assertEqual(l, [])
+
+
 def test_main():
     support.run_unittest(TestCase)
 
diff --git a/Misc/NEWS b/Misc/NEWS
index a7a3506..a0685d6 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -409,8 +409,12 @@
 Library
 -------
 
+- Issue #13449 sched.scheduler.run() method has a new "blocking" parameter which
+  when set to False makes run() execute the scheduled events due to expire
+  soonest (if any) and then return.  Patch by Giampaolo Rodolà.
+
 - Issue #8684 sched.scheduler class can be safely used in multi-threaded
-  environments.
+  environments.  Patch by Josiah Carlson and Giampaolo Rodolà.
 
 - Alias resource.error to OSError ala PEP 3151.