We propose two multicast routing algorithms in this paper. One is a delay-constrained multicast algorithm that finds a multicast tree between one source node and multiple destination nodes. The other is a dynamic multicast algorithm that allows multiple nodes to dynamically join or leave a multicast group during a session. The first algorithm, which provides multicasting and guaranteed QoS(Quality-of-Service) services at the network layer, is a distributed routing algorithm where the reduced multicast tree is computed through a single round of message exchanges between network nodes, consequently reducing the number of messages and the accompanying computation time. The distributed algorithm is shown to generate within much less time a multicast tree slightly more expensive than that by the centralized one. The second algorithm is efficient under dynamic network environment, with frequent status changes for network nodes or links and multicast group members.