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This paper examines some issues that affect the efficiency and fairness of the Transmission Control Protocol (TCP), the backbone of Internet protocol communication, in multihops satellite network systems. It proposes a scheme that allows satellite systems to automatically adapt to any change in the number of active TCP flows due to handover occurrence, the free buffer size, and the bandwidth-delay product of the network.The proposed scheme has two major design goals: increasing the system efficiency, and improving its fairness. The system efficiency is controlled by matching the aggregate traffic rate to the sum of the link capacity and total buffer size. On the other hand, the system min-max fairness is achieved by allocating bandwidth among individual flows in proportion with their RTTs. The proposed scheme is dubbed Recursive, Explicit, and Fair Window Adjustment (REFWA).Simulation results elucidate that the REFWA scheme substantially improves the system fairness, reduces the number of packet drops, and makes better utilization of the bottleneck link. The results demonstrate also that the proposed scheme works properly in more complicated environments where connections traverse multiple bottlenecks and the available bandwidth may change over data transmission time.