Many new multimedia applications involve dynamic multiple participants, have stringent endto-end delay requirement and consume large amount of network resources. In this paper, we propose a new dynamic delay-constrained least-cost multicast routing algorithm (DDCLCMR) to support these applications. When group membership changes, the existing multicast tree is perturbed as little as possible. Simulation results show that DDCLCMR performs very good in terms of cost for both, static and dynamic multicast groups, when compared to the best multicast algorithms known.