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This paper discusses the multicast routing problem with multiple QoS constraints, which may deal with the delay, delay jitter, bandwidth and packet loss metrics, and describes a network model for researching the routing problem. It presents a distributed multicast routing protocol (DMRP). The DMRP attempts to significantly reduce the overhead of constructing a multicast tree with multiple QoS constraints. In DMRP, a multicast group member can join or leave a multicast session dynamically, which should not disrupt the multicast tree. It also attempts to minimize overall cost of the tree, and satisfy the multiple QoS constraints and least cost's (or lower cost) requirements. The proof of correctness and complexity analysis of the DMRP are also given. Simulation results show that DMRP is an available approach to multicast routing decision for dynamic network with multiple QoS constraints.