diff --git a/rest_framework/permissions.py b/rest_framework/permissions.py
index 3a8c580646..f880fcc254 100644
--- a/rest_framework/permissions.py
+++ b/rest_framework/permissions.py
@@ -48,39 +48,37 @@ def __call__(self, *args, **kwargs):
 
 
 class AND:
-    def __init__(self, op1, op2):
-        self.op1 = op1
-        self.op2 = op2
+    def __init__(self, *args):
+        self.permissions = args
 
     def has_permission(self, request, view):
-        return (
-            self.op1.has_permission(request, view) and
-            self.op2.has_permission(request, view)
-        )
+        for permission in self.permissions:
+            if not permission.has_permission(request, view):
+                return False
+        return True
 
     def has_object_permission(self, request, view, obj):
-        return (
-            self.op1.has_object_permission(request, view, obj) and
-            self.op2.has_object_permission(request, view, obj)
-        )
+        for permission in self.permissions:
+            if not permission.has_object_permission(request, view, obj):
+                return False
+        return True
 
 
 class OR:
-    def __init__(self, op1, op2):
-        self.op1 = op1
-        self.op2 = op2
+    def __init__(self, *args):
+        self.permissions = args
 
     def has_permission(self, request, view):
-        return (
-            self.op1.has_permission(request, view) or
-            self.op2.has_permission(request, view)
-        )
+        for permission in self.permissions:
+            if permission.has_permission(request, view):
+                return True
+        return False
 
     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)
-        )
+        for permission in self.permissions:
+            if permission.has_object_permission(request, view, obj):
+                return True
+        return False
 
 
 class NOT: