A loop transmission system consisting of a central station, N input terminals with infinite buffer, and a multiplexed channel is considered. Data flows from the terminals to the central station and from the central station to the terminals. The first type of data transfer is accorded priority over the second type. This necessitates intermediate buffering of data from the central station to the terminals. The distributions of the queue lengths at all terminals and of the virtual waiting times of data units are calculated. Two numerical examples are given. © 1973 Academic Press, Inc.