Summary: During prolonged temporal isolation in caves or windowless rooms, human subjects often develop complicated sleep-wake patterns. Seeking lawful structure in these patterns, we have reanalyzed the spontaneous timing of 359 sleep-wake cycles recorded from 15 internally desynchronized human subjects. The observed sleep-wake patterns obey a simple rule: The phase of the circadian temperature rhythm at bedtime determines the lengths of both prior wake (ex) and subsequent sleep (p). From this rule we derive an average ex:p relationship that depends on circadian phase. The relationship reconciles the established negative ex:p correlation observed in synchronized subjects with the positive ex:p correlation found in desynchronized subjects. Our most surprising result concerns the residual deviations of ex and p from their circadian phase-adjusted mean values. We report that there is no significant positive correlation between the residuals of ex and p, contrary to the prediction of restorative models of sleep duration. Our findings illuminate the mechanisms underlying sleep regulation and provide much-needed tests of mathematical models of the sleep-wake cycle. Key Words: Circadian-Sleep-wake-Serial correlation -Mathematical model-Humans.To better understand how human sleep is regulated, many researchers have studied the sleep-wake behavior of subjects living for weeks in unscheduled, time-free environments (1-9). These experiments have taken place in underground caves (6)(7)(8), bunkers (1,2,5), or soundproofed, windowless apartments (3,9). A common finding is that subjects frequently go to bed near the minimum of their circadian temperature cycle. The sleep-wake and temperature rhythms then remain synchronized at a period near 25 h. Aschoff (1) reported the striking phenomenon of spontaneous internal desynchronization, in which subjects unintentionally but repeatedly stay up past the temperature minimum, leading to average sleep-wake cycle lengths of 30-40 h. Sleep then occurs at unusual phases in the circadian temperature cycle, with concomitant changes in its internal organization (4).Many mathematical models of the human sleep-wake cycle (10-13) have been proposed recently. Nearly all manage to simulate the qualitative aspects of internal de-