Results are reported of four analyses of the distribution of REM sleep across nights of two subjects who slept for 50 consecutive nights on a regimented, but normal, sleep schedule. We found (a) a strong phase-setting effect of sleep onset on the distribution of REM sleep within nights, (b) no systematic change in the phase of the distribution of REM sleep across nights, and (c) a relationship between the nocturnal temperature minimum and the distribution of REM sleep within nights. Our results are consistent with the notion that the nightly distribution of REM sleep may be determined by an oscillatory process, the phase of which is reset at sleep onset, but which may be subject to other influences, such as the circadian temperature rhythm. These results are in general agreement with those found by investigators studying subjects on free-running or other abnormal sleep schedules.