ATM networks are intended to accommodate all traffic types, including highly bursty traffic. In this paper, we present a traffic control framework for handling bursty traffic on a burst-by-burst basis. The protocol and associated mechanisms are designed to handle bursts of related cells as units. Hence, cells in a burst are forwarded or dropped as a unit. The framework includes mechanisms to allow a connection to acquire resources at a switch when a burst arrives and to release them when a burst leaves. In addition, techniques for bundling such bursty connections into virtual paths are described. A candidate burst-oriented call admission control scheme is also presented. The performance of the burst-oriented approach is then analyzed.