diff --git a/rest_framework/permissions.py b/rest_framework/permissions.py
index 5d75f54ba..56ed5af5d 100644
--- a/rest_framework/permissions.py
+++ b/rest_framework/permissions.py
@@ -81,8 +81,9 @@ class OR:
 
     def has_object_permission(self, request, view, obj):
         return (
-            self.op1.has_object_permission(request, view, obj) or
-            self.op2.has_object_permission(request, view, obj)
+            (self.op1.has_permission(request, view) and self.op1.has_object_permission(request, view, obj))
+            or
+            (self.op2.has_permission(request, view) and self.op2.has_object_permission(request, view, obj))
         )