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Multicasting in Diffserv networks is a challenging problem due to the architectural conflicts between them, namely, stateful vs. stateless core. In this paper, we assume an edge-based multicast (EBM) model wherein the multicast tree is constructed such that the branching occurs only at the edge routers. We propose an algorithm to solve the problem of dynamic member join/leave in heterogeneous QoS multicasting under EBM model. We formally state the problem and propose an algorithm for it, which is optimal when the constraint on the member join/leave requires that there can be no service disruption for on-tree nodes. We then evaluate the performance of our algorithm with respect to a static multicast tree construction heuristic and a source-based shortest path algorithm using "tree QoS cost" as a primary metric. Our studies show that the proposed algorithm achieves good performance in terms of tree QoS cost, time taken for member join/leave, and number of service disruptions with acceptable storage overhead.