A brief overview of models on the regulation of sleep/waking or rest/activity is provided. Applications of the two-process model are illustrated in two species: The homeostatic facet of the model (Process S) was used to quantitatively simulate sleep in the rat and guinea pig. The model parameters were estimated for rat sleep by an optimization procedure. A close correspondence between the time course of slow-wave activity and Process S was obtained for both species under baseline conditions. Whereas in the rat a close fit was obtained also for the recovery period from sleep deprivation, some discrepancies were present in the guinea pig. It is concluded that the concept of sleep homeostasis that has been elaborated and formalized in the two-process model for human sleep, can also be applied to simulate sleep in other mammals.