With the increasing use of distributed hard real-time systems, the ability of computer networks to handle hard real-time message traffic is becoming more important. For traditional networks, maximizing the throughput or minimizing the average message delay is the most important performance criteria. In the hard real-time domain, however, concern focuses on satisfying the time constraints of individual messages. This paper examines recent developments in hard real-time communication in local area multiple-access networks. Two general strategies are used in hard real-time communication: the guarantee strategy and the best-effol~ strategy. In the former, messages are guaranteed to meet their deadlines during normal operation of the network. In the best-effort strategy, the network will attempt to send messages before their deadlines, but no guarantees are given. Real-time message traffic can be distinguished according to whether it is best suited for the guarantee strategy or the best-effort strategy. Although this paper concentrates on multiple-access networks, many of the concepts presented and lessons learned are also applicable to other types of networks. COMMUNICATION IN MULTIPLE-ACCESS NEWTWORKS 49