Although the magnitude of lateral inhibition in the retina of Limulus polyphemus depends strongly on the distance between ommatidia, the time of delay tau between the response of one ommatidium and the consequent inhibition of another is independent of the distance between them and is approximately 0.1 sec. Moreover, experimental observations indicate that for intact undamaged retinae in intense spatially uniform illumination, the total inhibitory influence at a given ommatidium can exceed the excitation of that ommatidium. A simple theory combining these two known facts yields the following conclusions: The response of a healthy Limulus retina to an intense, temporally constant, and spatially uniform excitation e (in the usual Hartline-Ratliff units) should be a sustained synchronous oscillation of period 2tau, with the mean response over one complete cycle equal to approximately 1/2e. Under a broad class of circumstances the sustained oscillations should take the form of a succession of "bursts" and "rest periods", each of duration tau. The oscillations can have, however, a fine structure in which there is repeated information about the duration and sequence of any short pulses of excitation which occurred within a time-interval of length tau before the onset of steady excitation. Because it is repeated every 2tau seconds, this information remains available in the retina for interaction with subsequent changes of excitation.