diff --git a/Lib/asyncio/unix_events.py b/Lib/asyncio/unix_events.py
index a55b3a375fa22d7..dfdbb3aff89859c 100644
--- a/Lib/asyncio/unix_events.py
+++ b/Lib/asyncio/unix_events.py
@@ -63,6 +63,7 @@ class _UnixSelectorEventLoop(selector_events.BaseSelectorEventLoop):
     def __init__(self, selector=None):
         super().__init__(selector)
         self._signal_handlers = {}
+        self._old_handlers = {}
 
     def close(self):
         super().close()
@@ -113,7 +114,11 @@ def add_signal_handler(self, sig, callback, *args):
             # Register a dummy signal handler to ask Python to write the signal
             # number in the wakeup file descriptor. _process_self_data() will
             # read signal numbers from this file descriptor to handle signals.
-            signal.signal(sig, _sighandler_noop)
+            old_handler = signal.signal(sig, _sighandler_noop)
+
+            if callable(old_handler):
+                # Store the previous handler as well so we can call it later.
+                self._old_handlers[sig] = old_handler
 
             # Set SA_RESTART to limit EINTR occurrences.
             signal.siginterrupt(sig, False)
@@ -140,6 +145,11 @@ def _handle_signal(self, sig):
         else:
             self._add_callback_signalsafe(handle)
 
+        old_handler = self._old_handlers.get(sig)
+
+        if old_handler:
+            old_handler(sig, (None, "sorry, no stack available, greetings from asyncio/unix_events"))
+
     def remove_signal_handler(self, sig):
         """Remove a handler for a signal.  UNIX only.
 
diff --git a/Misc/NEWS.d/next/Library/2021-05-22-01-12-14.bpo-44212.RXiAsf.rst b/Misc/NEWS.d/next/Library/2021-05-22-01-12-14.bpo-44212.RXiAsf.rst
new file mode 100644
index 000000000000000..1883b6f9ebcf636
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-05-22-01-12-14.bpo-44212.RXiAsf.rst
@@ -0,0 +1,2 @@
+asyncio: signal handlers registered by add_signal_handler() now call
+previously registered handlers (if any).