The question of the serial dependence of successive REM-NREM sleep cycles was examined. The experiments were performed in two different settings: 309 sleep episodes of 11 healthy young sleepers (age range, 20-36 years) were recorded under entrained conditions in the sleep laboratory; 5 of these subjects also slept in an isolation unit (underground apartment) with free-running sleep-wake cycles for a total of 107 sleep episodes. The covariances between the first three REM-NREM cycles were computed using an intraindividual cross-night approach. Significant negative covariances were observed. This result confirmed the assumption of serial dependencies between successive REM-NREM cycles. These data agree with the features of a periodically driven process and are incompatible with the alternatively hypothesized renewal model. The periodically driven process is similar in concept to the basic rest-activity cycle.