Sleep structure in the rat was characterized during uninterrupted full-day recordings using an analytic procedure that identifies rapid eye movement (REM) sleep episodes based on REM-sleep-onset electroencephalograph phenomena, hence independently of REM-sleep duration. The data were used to determine whether REM-sleep timing is controlled homeostatically or by an oscillatory mechanism. The findings and conclusions are that 1) non-REM (NREM) sleep episode duration is positively correlated with prior REM-sleep episode duration, suggesting that REM-sleep expression is permissive of NREM sleep; 2) mean NREM-sleep episode duration decreases after repeated brief REM-sleep episodes (< 30 s), also suggesting that discharge of REM-sleep propensity is essential for NREM-sleep expression; 3) REM-sleep episode duration is independent of prior sleep history, suggesting that REM-sleep maintenance is controlled by factors other than accumulated REM-sleep propensity; 4) brief REM-sleep episodes occur progressively more frequently over the course of the NREM-sleep interval between sustained REM-sleep episodes (> 30 s), suggesting that REM-sleep propensity increases progressively within episodes of NREM sleep; and 5) the diurnal cycle of REM-sleep expression primarily reflects modulation in the efficiency of REM-sleep maintenance. These findings support the hypothesis that REM-sleep timing is controlled by accumulation of REM-sleep propensity during NREM sleep.