diff --git a/packages/google-cloud-resource-manager/setup.py b/packages/google-cloud-resource-manager/setup.py
index 5d7fd829dfbd..b24ad370d079 100644
--- a/packages/google-cloud-resource-manager/setup.py
+++ b/packages/google-cloud-resource-manager/setup.py
@@ -29,8 +29,8 @@
 # 'Development Status :: 5 - Production/Stable'
 release_status = 'Development Status :: 3 - Alpha'
 dependencies = [
-    'google-cloud-core<0.29dev,>=0.28.0',
-    'google-api-core<2.0.0dev,>=0.1.1',
+    'google-api-core >= 1.0.0, < 2.0.0dev',
+    'google-cloud-core >= 0.28.0, < 0.29dev',
 ]
 extras = {
 }