Pairs of neurons which inhibit each other can produce regular alternating bursts of impulses if they also exhibit postinhibitory rebound (PIR). Computer studies show that stable patterns occur spontaneously in systems of pacemaker neurons with PIR, and can be triggered in systems of nonpacemakers without requiring tonic excitation. The repetition rates of these patterns are determined largely by the PIR parameters. The patterns resist perturbation by phasic synaptic inputs, but can be modulated or turned off by tonic inputs. One pair of PIR neurons can be entrained by another pair with a different repetition rate to produce more complex firing patterns.