A new policy for routing in A TM networks is introduced. Virtual circuits are routed at call set-up level, by combining Call Admission Control (CAC) and routing decisions in a hop-by-hop fashion at the nodes along a path. The network traffic is divided into classes, homogeneous with respect to performance requirements and statistical characteristics, which are dynamically assigned bandwidth partitions over the network links, by means of scheduling algorithms at the switching nodes. At each node traversed, a call request of a certain class is first assigned a subset of outgoing links towards the destination, upon which the resources necessary to maintain the required level of Quality of Service (QoS) are available; then, a routing decision is taken, by choosing the least "cost" link, according to a specific criterion. The link costs are dynamically updated for all traffic classes, by means of local information and of aggregate information exchanged among neighbouring nodes, and are based on a measure of the link "saturation", in terms of some "distance" from the boundary of the load region in call-space that the multiplexer serving the link can support. In case that no route is available at a node, the call request is traced back to the least-loaded node (according to the measure chosen) among the ones already visited along the path. This strategy is analysed and compared by simulation, in terms of performance and of the capability of reacting to network failures, with a previous one that immediately drops the call at the node where blocking occurs. Keywords A TM, routing.