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This paper presents two admission control policies for a new communications application named voice message service (VMS) in mobile cellular networks. In circuit-switching systems, a trunk reservation scheme is proposed for the admission of real-time VMS. In integrated voice and data networks, VMS is considered a nonreal-time traffic and a preemptive priority scheme is applied. The system is modeled by a two dimensional Markov chain. The performance of the admission policies is measured in terms of the call blocking and dropping probabilities of voice calls and the average number of queueing VMS requests.