Synaptic depression is a form of short-term plasticity exhibited by many synapses. Nonetheless, the functional significance of synaptic depression in oscillatory networks is not well understood. We show that, in a recurrent inhibitory network that includes an intrinsic oscillator, synaptic depression can give rise to two distinct modes of network operation. When the maximal conductance of the depressing synapse is small, the oscillation period is determined by the oscillator component. Increasing the maximal conductance beyond a threshold value activates a positive-feedback mechanism that greatly enhances the synaptic strength. In this mode, the oscillation period is determined by the strength and dynamics of the depressing synapse. Because of the regenerative nature of the feedback mechanism, the circuit can be switched from one mode of operation to another by a very small change in the maximal conductance of the depressing synapse. Our model was inspired by experimental work on the pyloric network of the lobster. The pyloric network produces a simple motor rhythm generated by a pacemaker neuron that receives feedback inhibition from a depressing synapse. In some preparations, elimination of the synapse had no effect on the period of the rhythm, whereas in other preparations, there was a significant decrease in the period. We propose that the pyloric network can operate in either of the two modes suggested by the model, depending on the maximal conductance of the depressing synapse.