<p><b>Abstract</b>—Unlike deterministic real-time communication in which excessive resources may be required for “absolute” performance guarantees, statistical real-time communication seeks to achieve <it>both</it> probabilistic performance guarantees and efficient resource sharing. This paper presents a framework for statistical real-time communication in ATM networks, providing delay-guaranteed transport of MPEG-coded video traffic with a statistically-guaranteed cell-loss ratio. Delay-guaranteed communication is achieved with a modified version of Traffic-Controlled Rate-Monotonic Priority Scheduling (TCRM). A set of statistical real-time channels that share similar traffic characteristics are multiplexed into a common <it>macrochannel</it>. Those statistical real-time channels which are multiplexed together share the resources of a macrochannel, and individual statistical real-time channels are given timeliness and probabilistic cell-loss guarantees. A macrochannel is serviced by the modified TCRM which improves link utilization and makes channel management simpler. Based on the analysis of an <tmath>$M/D/1/N$</tmath> queueing system, we propose a procedure for determining the transmission capacity of a macrochannel necessary to statistically guarantee a cell-loss ratio bound. Our extensive trace-driven simulation has shown the superiority of the proposed framework to the other approaches. The overall cell-loss ratios for <it>multihop</it> statistical real-time channels are shown to be smaller than the predetermined bounds, thus verifying our analytical results.</p>