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The availability of bandwidth resources fluctuates much more severely in mobile communication networks compared to wired networks. There is a growing interest in developing adaptive multimedia services in mobile communication networks, where it is possible to increase or decrease the bandwidth of individual ongoing flows. This paper studies the issues of call admission control and bandwidth adaptation in such systems. We present a novel approach that models the system as a Markov decision process, and uses a form of reinforcement learning to solve the call admission control and bandwidth adaptation problems without the knowledge of the state transition probabilities. More realistic assumptions can therefore be applied to the underlying system model for this approach than in the previous schemes. Simulation results demonstrate the effectiveness of the proposed scheme in adaptive multimedia mobile communication networks.