Swimmerets move periodically through a cycle of power-strokes and return-strokes. Swimmerets on neighboring segments differ in phase by approximately 25%, and maintain this difference even when the period of the cycle changes from < 1 to > 4 Hz. We constructed a minimal cellular model of the segmental pattern-generating circuit which incorporated its essential components, and whose dynamics were like those of the local circuit. Three different intersegmental coordinating units were known to link neighboring ganglia, but their targets are unknown. We constructed different intersegmental circuits which these units might form between neighboring cellular models, and compared their dynamics with the real system. One intersegmental circuit could maintain an approximately 25% phase difference through a range of periods. In physiological experiments, we identified three types of intersegmental interneurons that originate in each ganglion and project to its neighbors. These neurons fire bursts at certain parts of the swimmeret cycle in their home ganglion. These three neurons are necessary and sufficient to maintain normal coordination between neighboring segments. Their properties conform to the predictions of the cellular model.