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Several low Earth orbit (LEO) satellite constellations have been proposed for mobile satellite systems (MSS). Due to nonstationary coverage regions of individual LEO satellites, the offered traffic load for each cell varies continuously. The variation of the traffic load essentially requires dynamic channel assignment. Furthermore, extremely frequent handover requests require specific techniques that prioritize the service of handover requests. In this paper, we suggest a new dynamic channel assignment (DCA) scheme which eliminates forced call terminations due to handover failure (call dropping). This scheme utilizes frequency spectrum efficiently, and can also provide users a high-quality premium service that guarantees the success of each handover procedure, called guaranteed handover service. This is based on position measurement. Finally, we compare our algorithm with some other DCA algorithms by computational experiments. The results of the experiments show that our algorithm provides systems with higher throughput (higher completed call ratio) as well as guaranteed handovers.