In high-speed communication networks, large propagation delays could have an adverse impact on the stability of feedback control algorithms. In this paper, classical control theory and Smith's principle are exploited to design an algorithm for controlling "best effort" traffic in high-speed asynchronous transfer mode (ATM) networks. The designed algorithm guarantees the stability of network queues, along with the fair and full utilization of network links, in a realistic traffic scenario in which multiple available bit rate (ABR) connections, with different propagation delays, share the network with high priority traffic.