In cats, rats, and mice, the amount of rapid eye movement sleep (REMS) lost during a sleep deprivation (SD) predicts the subsequent REMS rebound during recovery sleep. This suggests that REMS is homeostatically regulated and that a need or pressure for REMS accumulates in its absence, i.e. during both wakefulness and non-rapid eye movement sleep (NREMS). Conversely, it has been proposed that REMS pressure accumulates exclusively during NREMS [Benington and Heller, Am. J. Physiol. 266 (1994) R1992; Prog. Neurobiol. 44 (1994b) 433]. This hypothesis is based on the analysis of the duration of successive NREMS and REMS episodes and of electroencephalogram (EEG) events preceding REMS. Pre-REMS events (PREs) do not always result in sustained REMS and can thus be regarded as REMS attempts that increase as NREMS progresses. It is assumed that two processes regulating REMS can resolve the apparent contradiction between these two concepts: a `long-term' process that homeostatically regulates the daily REMS amount and a `short-term' process that regulates the NREM–REMS cycle. These issues were addressed in two SD experiments in rats. The two SDs varied in length (12 and 24 h) and resulted in very similar compensatory changes in NREMS but evoked very different changes for all REMS parameters studied. The large REMS increase observed after 24-h SD was accompanied by a reduction in unsuccessful PREs and an increase in sustained REMS episodes, together resulting in a threefold increase in the success-rate to enter REMS. Changes in success-rate matched those of a theoretically derived long-term REMS pressure. The SD induced changes in sleep architecture could be reproduced by assuming that the increased long-term REMS pressure interacts with the short-term process by increasing the probability to enter and remain in REMS.