Recent experimental studies investigating the neuronal regulation of rapid eye movement (REM) sleep have identified mutually inhibitory synaptic projections among REM sleep-promoting (REM-on) and REM sleep-inhibiting (REM-off) neuronal populations that act to maintain the REM sleep state and control its onset and offset. The control mechanism of mutually inhibitory synaptic interactions mirrors the proposed flip-flop switch for sleep-wake regulation consisting of mutually inhibitory synaptic projections between wake- and sleep-promoting neuronal populations. While a number of synaptic projections have been identified between these REM-on/REM-off populations and wake/sleep-promoting populations, the specific interactions that govern behavioral state transitions have not been completely determined. Using a minimal mathematical model, we investigated behavioral state transition dynamics dictated by a system of coupled flip-flops, one to control transitions between wake and sleep states, and another to control transitions into and out of REM sleep. The model describes the neurotransmitter-mediated inhibitory interactions between a wake- and sleep-promoting population, and between a REM-on and REM-off population. We proposed interactions between the wake/sleep and REM-on/REM-off flip-flops to replicate the behavioral state statistics and probabilities of behavioral state transitions measured from experimental recordings of rat sleep under ad libitum conditions and after 24 h of REM sleep deprivation. Reliable transitions from REM sleep to wake, as dictated by the data, indicated the necessity of an excitatory projection from the REM-on population to the wake-promoting population. To replicate the increase in REM-wake-REM transitions observed after 24 h REM sleep deprivation required that this excitatory projection promote transient activation of the wake-promoting population. Obtaining the reliable wake-nonREM sleep transitions observed in the data required that activity of the wake-promoting population modulated the interaction between the REM-on and REM-off populations. This analysis suggests neuronal processes to be targeted in further experimental studies of the regulatory mechanisms of REM sleep.