diff --git a/setup.py b/setup.py
index fd62b720..d395e71f 100644
--- a/setup.py
+++ b/setup.py
@@ -31,8 +31,8 @@
     # Note: google-api-core and google-auth are also included via transitive
     # dependency on google-cloud-bigquery, but this library also uses them
     # directly.
-    "google-api-core >=1.21.0",
-    "google-auth >=1.18.0",
+    "google-api-core >= 1.31.5, <3.0.0dev,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.0",
+    "google-auth >=1.25.0",
     "google-auth-oauthlib >=0.0.1",
     # Require 1.27.* because it has a fix for out-of-bounds timestamps.  See:
     # https://github.com/googleapis/python-bigquery/pull/209 and
diff --git a/testing/constraints-3.7.txt b/testing/constraints-3.7.txt
index f0c9a4ac..2d4674eb 100644
--- a/testing/constraints-3.7.txt
+++ b/testing/constraints-3.7.txt
@@ -6,8 +6,8 @@
 # e.g., if setup.py has "foo >= 1.14.0, < 2.0.0dev",
 # Then this file should have foo==1.14.0
 db-dtypes==0.3.1
-google-api-core==1.21.0
-google-auth==1.18.0
+google-api-core==1.31.5
+google-auth==1.25.0
 google-auth-oauthlib==0.0.1
 google-cloud-bigquery==1.27.2
 google-cloud-bigquery-storage==1.1.0