diff --git a/oslo_service/__init__.py b/oslo_service/__init__.py
index 2da3fca7..1529e7d1 100644
--- a/oslo_service/__init__.py
+++ b/oslo_service/__init__.py
@@ -13,7 +13,6 @@
 import os
 
 import eventlet.patcher
-import monotonic
 from oslo_log import log as logging
 
 time = eventlet.patcher.original('time')
@@ -27,6 +26,7 @@ if hasattr(time, 'monotonic'):
     # Use builtin monotonic clock, Python 3.3+
     _monotonic = time.monotonic
 else:
+    import monotonic
     _monotonic = monotonic.monotonic
 
 
diff --git a/oslo_service/periodic_task.py b/oslo_service/periodic_task.py
index f8d4abc3..caa99e40 100644
--- a/oslo_service/periodic_task.py
+++ b/oslo_service/periodic_task.py
@@ -16,7 +16,11 @@ import logging
 import random
 import time
 
-from monotonic import monotonic as now  # noqa
+if hasattr(time, 'monotonic'):
+    now = time.monotonic
+else:
+    from monotonic import monotonic as now  # noqa
+
 from oslo_utils import reflection
 import six
 
diff --git a/requirements.txt b/requirements.txt
index 9e71d4c8..08537f0f 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -5,7 +5,7 @@
 WebOb>=1.7.1 # MIT
 eventlet!=0.18.3,!=0.20.1,>=0.18.2 # MIT
 greenlet>=0.4.10 # MIT
-monotonic>=0.6 # Apache-2.0
+monotonic>=0.6;python_version<'3.3'  # Apache-2.0
 oslo.utils>=3.33.0 # Apache-2.0
 oslo.concurrency>=3.25.0 # Apache-2.0
 oslo.config>=5.1.0 # Apache-2.0