Rhythmic muscular contractions are essential for many different behaviors, from locomotion to respiration. These behaviors are modulated by changes in the external environment, such as temperature shifts and presence of predators, and by internal states, such as hunger and sleep. The roundworm Caenorhabditis elegans feeds on bacteria through rhythmic contraction and relaxation of its pharynx, a neuromuscular pump innervated by a nearly independent network of just 20 neurons. Feeding rate is modulated by many environmental and physiological factors, but feeding generally persists throughout the life of the worm, ceasing only during sleep. The mechanisms by which the pharyngeal nervous system controls feeding during wake and sleep are poorly understood. I used optogenetics, genetics, and pharmacology to define the cholinergic pharyngeal circuitry that regulates feeding rate during wake, and then used similar approaches to examine how feeding is inhibited during sleep. I identified a four-neuron circuit that regulates feeding rate during wake and found that it is degenerate, meaning that multiple different classes of neurons can stimulate feeding in a similar manner. I also found that feeding quiescence is generated by distinct mechanisms during two behaviorally indistinguishable sleep states: cholinergic motor neurons are inhibited during stress-induced sleep, while the muscle is directly inhibited during developmentally timed sleep. Thus, as in mammals and despite its behavioral homogeneity, sleep in C. elegans is not a physiologically homogenous state. These results provide insight into the function of a highly conserved neural circuit that generates robust rhythmic behavior, and illustrate how this circuit can be altered in different ways to produce the same behavioral output during two distinct sleep states.