diff --git a/setup.py b/setup.py
index 8fc04405e..7d70e25bc 100644
--- a/setup.py
+++ b/setup.py
@@ -37,6 +37,7 @@
 
 dependencies = [
     "grpcio >= 1.51.3, < 2.0dev",  # https://github.com/googleapis/python-pubsub/issues/609
+    # google-api-core >= 1.34.0 is allowed in order to support google-api-core 1.x
     "google-api-core[grpc] >= 1.34.0, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.*,!=2.4.*,!=2.5.*,!=2.6.*,!=2.7.*,!=2.8.*,!=2.9.*,!=2.10.*",
     "proto-plus >= 1.22.0, <2.0.0dev",
     "proto-plus >= 1.22.2, <2.0.0dev; python_version>='3.11'",