diff --git a/batch_test.go b/batch_test.go
index 31ddbc7e..c441abdd 100644
--- a/batch_test.go
+++ b/batch_test.go
@@ -597,6 +597,10 @@ func TestConnBeginBatchDeferredError(t *testing.T) {
 	conn := mustConnectString(t, os.Getenv("PGX_TEST_DATABASE"))
 	defer closeConn(t, conn)
 
+	if conn.PgConn().ParameterStatus("crdb_version") != "" {
+		t.Skip("Server does not support deferred constraint (https://github.com/cockroachdb/cockroach/issues/31632)")
+	}
+
 	mustExec(t, conn, `create temporary table t (
 		id text primary key,
 		n int not null,
diff --git a/query_test.go b/query_test.go
index b9119cf8..51ca36de 100644
--- a/query_test.go
+++ b/query_test.go
@@ -542,6 +542,10 @@ func TestConnQueryDeferredError(t *testing.T) {
 	conn := mustConnectString(t, os.Getenv("PGX_TEST_DATABASE"))
 	defer closeConn(t, conn)
 
+	if conn.PgConn().ParameterStatus("crdb_version") != "" {
+		t.Skip("Server does not support deferred constraint (https://github.com/cockroachdb/cockroach/issues/31632)")
+	}
+
 	mustExec(t, conn, `create temporary table t (
 	id text primary key,
 	n int not null,