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In this paper, we study the problem concerning how to construct a delay-constrained multicast tree with minimum power-consumption so that real-time multimedia applications can be supported in ad hoc wireless networks. Based on a number of link-replacing strategies, we present a heuristic called ELR algorithm for determining a multicast tree for the problem. Our ELR algorithm begins with a two-level multicast tree and then iteratively replaces the high-power links with lower-power links in order to reduce the total power required by the multicast tree. The simulation results show that for a given delay constraint the multicast tree found by our ELR algorithm requires less power than the one found by the previous published method.