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Multimedia applications involving real-time audio and/or video transmissions require strict QoS constraints (end-to-end delay bound, bandwidth availability and loss probability) to be met by the network. To guarantee real-time delivery of multimedia packets, a multicast channel needs to be established in advance using a path selection algorithm that takes into account the QoS constraints. In this paper we describe a distributed destination-controlled multicast routing (DCMR) protocol for multicasting with dynamic membership. DCMR establishes multicast connections in two stages, a forward routing stage, where setup messages carrying routing information are forwarded to the new destination, and a backward configuration stage, where the destination chooses a path with the highest available bandwidth under the delay constraint. Reservation is then attempted along this path backwards towards the multicast tree. Our simulations show that DCMR outperforms existing multicast routing algorithms in terms of call acceptance and connection setup time as it achieves low call blocking ratios