A hierarchical scheduling strategy for integrating real-time and non-real-time services in ATM networks is proposed. Provisions for satisfying the delay requirements of real-time CBR/VBR traffic and the throughput requirements of non-real-time ABR data traffic are provided. The approach uses known fair queueing schemes to implement fair bandwidth sharing amongst real-time connections and to provide minimum throughput guarantees for non-real-time traffic. Simulation results demonstrate that the hierarchical strategy meets the desired performance objectives and exhibits superior performance, both with respect to a flat scheduling hierarchy and a VBR priority approach.