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Resource allocation and call admission control (CAC) are two key issues in satellite networks for multimedia applications with quality of service (QoS) guarantees. This paper introduces a new priority-based CAC scheme for multiclass services in satellite networks operating above 10 GHz, where the dominant factor limiting performance is rain attenuation, a phenomenon exhibiting both spatial and temporal variation. The proposed scheme exploits the predictability of the satellite channel and accepts a new call if sufficient resources exist for existing and new users to guarantee their QoS requirements. At the same time, it assigns higher priority to real-time users compared to non-real time ones. The performance of the proposed scheme is investigated using Markov chain to represent the satellite channel states. Analytical expressions concerning the call blocking probability under clear sky and rain conditions are derived.