Connection oriented quality-of-service (QoS) based networks offer several service classes each designed to handle connections supporting various types of applications. A network failure will typically result in a large number of disrupted connections in each service class, all of which need to be restored simultaneously. In this paper we propose a distributed fault recovery priority scheme for dynamic restoration of connections. The proposed scheme exploits available network resources immediately after a failure together with properties of typical applications carried by the connections in order to give the applications sufficient network performance. The scheme is formulated within the context of switched virtual circuit routing in ATM networks, but it is applicable to ATM virtual path restoration as well and to other class based QoS networks like DiffServ MPLS based networks. The priority based restoration scheme is formulated as a centralized path flow integer programming optimization problem serving as a comparison benchmark for suboptimal distributed schemes. We propose a distributed heuristic scheme and give numerical results illustrating the quality of the proposed distributed scheme in comparison to the centralized optimal approach. Our numerical results show that the proposed distributed scheme can significantly improve utilization of network resources and enhance network performance after a failure.