Reciprocal inhibition between neuron pairs is a long-standing model for the mechanism by which circuits generate rhythmic animal movement patterns. This review shows that this model mechanism can explain the origins of cyclic movements in six different preparations for which the neuronal circuits are available. The overall function of reciprocal inhibition, when combined with a variety of dynamic properties in each of the circuits, is to generate stable antiphasic or multiphasic output patterns. Apparent redundancy in the identified circuits may lend additional robustness to the oscillations, but it also increases the difficulty of identifying critical circuit elements.