New technologies and the deployment of mobile and nomadic services are driving the emergence of complex communications networks, that have a highly dynamic behavior. This naturally engenders new route-discovery problems under changing conditions over these networks. Unfortunately, the temporal variations in the topology of dynamic networks are hard to be effectively captured in a classical graph model. In this paper, we use evolving graphs, which helps capture the dynamic characteristics of such networks, in order to compute multicast trees with minimum overall transmission time for a class of wireless mobile dynamic networks. We first show that computing different types of strongly connected components in evolving digraphs is NP-Complete, and then propose an algorithm to build all rooted directed minimum spanning trees in strongly connected dynamic networks. © Springer-Verlag Berlin Heidelberg 2003.