A class of discrete-time priority queueing systems with partial interference is considered. In these systems, N nodes share a common channel to transmit their packets. One node uses a random access scheme, while other nodes access the channel according to preassigned priorities. Packet arrivals are modeled as discrete-time batch processes, and packets are forwarded through the network according to fixed prescribed probabilities. Steady-state analysis of the class of systems under consideration is provided. In particular, we present a recursive method for the derivation of the joint generating function of the queue lengths distribution at the nodes in steady state. The condition for steady state is also derived. A simple example’ demonstrates the general analysis and provides some insights into the behavior of systems with partial interference such as multihop packet radio systems. Copyright © 1987 by The Institute of Electrical and Electronics Engineers, Inc.