SUMMARY The Limit Cycle Reciprocal Interaction Model (LCRIM) describes the stable interaction of REM-promoting and REM-antagonizing neurons which generates the periodic occurrence of REM sleep. The cycling of this physiological oscillator is subject to perturbation from excitatory input, referred to as E, which derives from other parts of the nervous system. An extended model is now proposed which combines the ultraradian REM regulation modelled by the LCRIM with the homeostatic regulation of slow-wave activity modelled by the Two-Process Models of Borbély, Achermann and Beersma. In addition, this integrated model extends the E construct to relate explicitly to both the REM and slow-wave sleep control systems, and to have stochastic dynamics. Overall, the model generates qualitatively realistic SWA, REM and wake-up patterns. However, its performance awaits quantitative validation.