Physiological knowledge of the neural mechanisms regulating sleep and wakefulness has been advanced by the recent findings concerning sleep/wakefulness-related preoptic/anterior hypothalamic and perifornical(orexin-containing)/posterior hypothalamic neurons. In this paper, we propose a mathematical model of the mechanisms orchestrating a quartet neural system of sleep and wakefulness composed of the following: 1) sleep-active preoptic/anterior hypothalamic neurons (N-R group); 2) wake-active hypothalamic and brainstem neurons exhibiting the highest rate of discharge during wakefulness and the lowest rate of discharge during paradoxical or rapid eye movement (REM) sleep (WA group); 3) brainstem neurons exhibiting the highest rate of discharge during REM sleep (REM group); and 4) basal forebrain, hypothalamic, and brainstem neurons exhibiting a higher rate of discharge during both wakefulness and REM sleep than during non-rapid eye movement (NREM) sleep (W-R group). The WA neurons have mutual inhibitory couplings with the REM and N-R neurons. The W-R neurons have mutual excitatory couplings with the WA and REM neurons. The REM neurons receive unidirectional inhibition from the N-R neurons. In addition, the N-R neurons are activated by two types of sleep-promoting substances (SPS), which play different roles in the homeostatic regulation of sleep and wakefulness. The model well reproduces the actual sleep and wakefulness patterns of rats in addition to the sleep-related neuronal activities across state-transitions. In addition, human sleep-wakefulness rhythms can be simulated by manipulating only a few model parameters: inhibitions from the N-R neurons to the REM and WA neurons are enhanced, and circadian regulation of the N-R and WA neurons is exaggerated. Our model could provide a novel framework for the quantitative understanding of the mechanisms regulating sleep and wakefulness.