With the emergence of multimedia applications, networks have to provide more and more bandwidth and should guarantee the quality of the communication between users. To address these issues, high speed architectures based on a virtual circuit model such as ATM have been designed and successfully implemented. The current trends in telecommunication deployment indicate that very large Internets based on such model will be available in the near future. This paper addresses the routing problem in this context and analyzes the existing solutions. It is concluded that the network has to provide precomputed and on-demand routes using a variation of the distance vector algorithm. Among other things, source routing and complete route recording are used to prevent loop formation.>