There are different priority classes of cells in ATM networks. The policing mechanisms seen in the literature only can police total traffic amount or total rate because they only use one token generator and one token pool In this paper, we only present six mechanisms using priority-classes of cells. All the policing mechanisms use two token generators and two token pools. They can distinguish the classes of arriving cells. They can police the rate of class-0 traffic as well as the total rate of the priority traffic. Their performances are studied through simulations.