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A NEtwork that is MObile (NEMO) usually consists of at least one Mobile Router (MR) attached to the infrastructure to manage all external communication for this moving network. Users inside a NEMO might also require quality of services (QoS) guarantee while accessing the Internet via a mobile device. In this paper, we propose a Bandwidth-sharing Reservation (BSR) scheme so that a NEMO can support QoS services. The proposed BSR scheme establishes a bandwidth sharing reservation tunnel for all NEMO nodes to efficiently utilize external bandwidth of MR, and it makes advance reservations at neighboring networks to solve the mobility problem. Three reservation adjustment policies are designed to further improve bandwidth utilization. Both mathematical analysis and simulation results show that the proposed BSR scheme can significantly increase bandwidth utilization and decrease handoff blocking rate while providing QoS services to NEMO nodes in movement.