Abstract: In multimedia communication networks, the multicasting is increasingly important. Nodes in the networks will likely vary in their abilities to support multicasting. Some nodes do not have multicasting ability, other nodes may be limited in the number of multicast copies they can reasonably make. So in this paper the degree-constraint of the node is used to represent its multicasting ability. Furthermore many services in networks require that the accumulated delay from the source node to every destination node can not exceed a pre-specified delay bound. In this paper the multicast routing algorithm with degree and delay constraints is proposed, and the Lagrange relaxation method is used to solve this problem.