Cellular mobile communication Networks have many services and each type of Services has distinct characteristics and Quality of Service requirement. It is important issues in 3-G and beyond networks are to prepare a framework for multiple class service, which performs call admission and handoff efficiently. There have been handful existing mechanisms for improving Call Admission Control (CAC) and Handoff Techniques in mobile network but most of them have considered only single class of service or might have touched value of few classes but not beyond. In this paper we have considered 8 types of services, which are differentiated according to their: Acceptable delay in transmission, Buffering capacity, Transmission mode and Bit rate. In this approach CAC and Handoff issues are resolved by awarding calls with some Priority Number by which each call will be recognized. Another issue of collision in CAC and handoff will be resolved by priority and authority to access the channel. Performance of this frame- work for CAC and Handoff is evaluated by calculating Call Dropping probability and Call Completion probability in this paper.