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The Motivation and goal of this paper is to propose dynamic distributed unicast and multicast routing algorithms for multiple classes of QoS guaranteed networks. In such networks we assume each link is able to provide multiple classes of QoS guarantee by reserving different amount of resource. In this paper, we tint propose a distributed unicast routing algorithm, DCSP (Distributed Constrained Shortest Path), to find a QoS constrained least cost path between each 0-D (Originating-Destination) pair. Two class reduction schemes, the linear and logarithmic policies, are proposed to avoid exponential growth of the number of end-to-end QoS classes. Based on DCSP, two distributed multicast routing algorithms, DCSPT (Distributed Constrained Shortest Path Tree) and DTM (Distributed Takahashi and Mutsuyama), are then proposed to find QoS constrained minimum cost trees. Our numerical results show that DCSP performs very well as compared to previously proposed centralized algorithms and it works better with the linear class reduction method. For the multicast routing algorithms, the DCSPT with linear class reduction algorithm yields the best performance.