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In this paper, we propose an adaptive bandwidth framework for supporting multiple classes of multimedia services with different quality of service (QoS) requirements in the next generation of wireless cellular networks. Three related components comprise the main building blocks of the framework. The core component is a threshold-based bandwidth allocation policy. The other two components are a call admission control algorithm and a bandwidth adaptation algorithm. The two algorithms are integrated into the framework to manage the network resources. We develop an analytical model to derive the QoS metrics new call blocking probability, handoff call dropping probability, and degradation probability. The model is based on a multi-dimensional Markov chain. The accuracy of the model is verified by comparison with simulation results. The simulation results show that the overall performance of our framework is very attractive in that the handoff call dropping probability is near zero (negligible).