diff --git a/simpervisor/atexitasync.py b/simpervisor/atexitasync.py
index 65aa954..d4869cb 100644
--- a/simpervisor/atexitasync.py
+++ b/simpervisor/atexitasync.py
@@ -8,27 +8,69 @@
 
 _handlers = []
 
+_prev_handlers = {}
 signal_handler_set = False
 
 
 def add_handler(handler):
-    global signal_handler_set
-    if not signal_handler_set:
-        signal.signal(signal.SIGINT, _handle_signal)
-        signal.signal(signal.SIGTERM, _handle_signal)
-        signal_handler_set = True
+    """
+    Adds a signal handler function that will be called when the Python process
+    receives either a SIGINT (on windows CTRL_C_EVENT) or SIGTERM signal.
+    """
+    _ensure_signal_handlers_set()
     _handlers.append(handler)
 
 
 def remove_handler(handler):
+    """Removes previously added signal handler."""
     _handlers.remove(handler)
 
 
+def _ensure_signal_handlers_set():
+    """
+    Ensures _handle_signal is registered as a top level signal handler for
+    SIGINT and SIGTERM and saves previously registered non-default Python
+    callable signal handlers.
+    """
+    global signal_handler_set
+    if not signal_handler_set:
+        # save previously registered non-default Python callable signal handlers
+        #
+        # windows note: signal.getsignal(signal.CTRL_C_EVENT) would error with
+        # "ValueError: signal number out of range", and
+        # signal.signal(signal.CTRL_C_EVENT, _handle_signal) would error with
+        # "ValueError: invalid signal value".
+        #
+        prev_sigint = signal.getsignal(signal.SIGINT)
+        prev_sigterm = signal.getsignal(signal.SIGTERM)
+        if callable(prev_sigint) and prev_sigint.__qualname__ != "default_int_handler":
+            _prev_handlers[signal.SIGINT] = prev_sigint
+        if callable(prev_sigterm) and prev_sigterm != signal.Handlers.SIG_DFL:
+            _prev_handlers[signal.SIGTERM] = prev_sigterm
+
+        # let _handle_signal handle SIGINT and SIGTERM
+        signal.signal(signal.SIGINT, _handle_signal)
+        signal.signal(signal.SIGTERM, _handle_signal)
+        signal_handler_set = True
+
+
 def _handle_signal(signum, *args):
+    """
+    Calls functions added by add_handler, and then calls the previously
+    registered non-default Python callable signal handler if there were one.
+    """
+    prev_handler = _prev_handlers.get(signum)
+
     # Windows doesn't support SIGINT. Replacing it with CTRL_C_EVENT so that it
     # can used with subprocess.Popen.send_signal
     if signum == signal.SIGINT and sys.platform == "win32":
         signum = signal.CTRL_C_EVENT
+
     for handler in _handlers:
         handler(signum)
-    sys.exit(0)
+
+    # call previously registered non-default Python callable handler or exit
+    if prev_handler:
+        prev_handler(signum, *args)
+    else:
+        sys.exit(0)
diff --git a/tests/child_scripts/signalprinter.py b/tests/child_scripts/signalprinter.py
index 61b583c..480f048 100644
--- a/tests/child_scripts/signalprinter.py
+++ b/tests/child_scripts/signalprinter.py
@@ -2,18 +2,30 @@
 Print received SIGTERM & SIGINT signals
 """
 import asyncio
+import signal
 import sys
 from functools import partial
 
 from simpervisor.atexitasync import add_handler
 
 
+def _non_default_handle(sig, frame):
+    # Print the received signum and then exit
+    print(f"non default handler received {sig}", flush=True)
+    sys.exit(0)
+
+
 def _handle_sigterm(number, received_signum):
     # Print the received signum so we know our handler was called
     print(f"handler {number} received", int(received_signum), flush=True)
 
 
 handlercount = int(sys.argv[1])
+# Add non default handler if arg true is passed
+if len(sys.argv) == 3:
+    if bool(sys.argv[2]):
+        signal.signal(signal.SIGINT, _non_default_handle)
+        signal.signal(signal.SIGTERM, _non_default_handle)
 for i in range(handlercount):
     add_handler(partial(_handle_sigterm, i))
 
diff --git a/tests/child_scripts/simplehttpserver.py b/tests/child_scripts/simplehttpserver.py
index cc460ff..44668cc 100644
--- a/tests/child_scripts/simplehttpserver.py
+++ b/tests/child_scripts/simplehttpserver.py
@@ -23,4 +23,4 @@ async def hello(request):
 
 app = web.Application()
 app.add_routes(routes)
-web.run_app(app, port=PORT)
+web.run_app(app, port=int(PORT))
diff --git a/tests/test_atexitasync.py b/tests/test_atexitasync.py
index 94e2fe1..866c6d2 100644
--- a/tests/test_atexitasync.py
+++ b/tests/test_atexitasync.py
@@ -49,3 +49,48 @@ def test_atexitasync(signum, handlercount):
     # The code should exit cleanly
     retcode = proc.wait()
     assert retcode == 0
+
+
+@pytest.mark.parametrize(
+    "signum, handlercount",
+    [
+        (signal.SIGTERM, 1),
+        (signal.SIGINT, 1),
+        (signal.SIGTERM, 5),
+        (signal.SIGINT, 5),
+    ],
+)
+@pytest.mark.skipif(
+    sys.platform == "win32",
+    reason="Testing signals on Windows doesn't seem to be possible",
+)
+def test_atexitasync_with_non_default_handlers(signum, handlercount):
+    """
+    Test signal handlers receive signals properly and handler existing default handlers
+    correctly
+    """
+    signalprinter_file = os.path.join(
+        os.path.dirname(os.path.abspath(__file__)), "child_scripts", "signalprinter.py"
+    )
+    proc = subprocess.Popen(
+        [sys.executable, signalprinter_file, str(handlercount), "true"],
+        stdout=subprocess.PIPE,
+        text=True,
+    )
+
+    # Give the process time to register signal handlers
+    time.sleep(1)
+    proc.send_signal(signum)
+
+    # Make sure the signal is handled by our handler in the code
+    stdout, stderr = proc.communicate()
+    expected_output = (
+        "\n".join([f"handler {i} received {signum}" for i in range(handlercount)])
+        + f"\nnon default handler received {signum}\n"
+    )
+
+    assert stdout == expected_output
+
+    # The code should exit cleanly
+    retcode = proc.wait()
+    assert retcode == 0