This paper is concerned with general loop systems in which each of several buffered units may exchange data with any other unit via a single oneway loop channel. The traffic is described in terms of stationary stochastic processes with independent increments. The queues of data waiting for transmission which develop at the different units are investigated. The queueing discipline assumed here accords data with longer transmission paths preemptive priority over those with shorter paths. For such systems expected queue lengths and waiting times in the steady state are calculated for all units and priority classes. An equivalence is established between general loop systems and systems of a much simpler structure and is used in the derivation. © 1975 Springer-Verlag.