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To provide truly global coverage needed by increased Personal Communication Services (PCS), a new generation of mobile satellite networks has been proposed. These low Earth orbit (LEO) mobile satellite networks handle multimedia traffic and can be used for non-real-time as well as real-time service to remote areas. Due to the many handoffs, resource management and connection admission control are important tasks for fair bandwidth sharing and QoS guarantees. Because the total link capacity has to be divided among several carriers and given the limited buffer capacity of the ATM switch, resource management is vital. It ensures the ability of the network to provide users with their negotiated QoS while protecting the network and the end-systems from congestion. We introduced a simple connection admission control (CAC) priority policy based on the delay and cell loss requirements for the investigated types of traffic. We took into account the handoff status of the satellite beams involved. Thus, we propose an onboard buffer architecture with separated buffers for new calls and intra-satellite handoff calls. The priority scheme applied is as follows: highest priority is given to CBR, followed by rt-VBR, nrtVBR and ABR.