In the near future a collection of data communication networks (the Internet) is going to provide a variety of services through multiple service classes where each service class will provide a different performance in terms of response time. These service classes will be designed to provide appropriate levels of service to user applications. This paper presents a priority pricing scheme which can be used to manage such a network. Each priority class may be mapped to one or more service classes. The approach presented in this paper can be implemented in a completely decentralized environment. Some simulation results using a hypothetical network with different service levels and requirements are also presented. These results indicate that priority pricing improves the performance significantly as compared to free access (or no usage base pricing) and flat pricing. The implementation of this priority pricing scheme is a practical solution to incentive compatibility in a network with diverse and unobservable user characteristics.