The periodic alternation between REM and NREM sleep was analyzed. Usually, sleep records of consecutive nights of a subject are regarded to be independent events. However, it may be that consecutive nights are realizations of a continuously ongoing rhythm. This was tested in the present study. The temporal patterns of REM and NREM sleep in sequences of about 30 consecutive nights for 3 subjects were analyzed. The results show that only the onset of the first REM sleep phase during any one night may be predicted from the sleep onset time, whereas a systematic phase shift between consecutive nights was observed in the later REM sleep phases. Thus, the onset of later REM sleep phases is better predicted by assuming a rhythm with stable period length which controls the appearance of REM sleep phases in successive nights. Under the experimental conditions the phase shift was between 5 and 10 min per 24 hrs for the 3 subjects. The result is accordance with Kleitman's basic rest activity cycle (BRAC) hypothesis.