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We consider several classes of interfering queues that appear in packet-radio networks. We analyze the class of systems where one of the queues is given full priority and obtain an expression for the joint probability distribution of the queue lengths. For ALOHA-type systems with two symmetric queues we calculate the average packet waiting time and queue lengths, and for symmetric systems with an arbitrary number of subscribers we develop a method to approximate these quantities. The approximation turns out to be close to the analysis and simulation results.