Sleep is ubiquitous in the animal kingdom, yet our understanding of its possible functions, its control and evolution, remains rudimentary. Two main sleep states have traditionally been distinguished in mammals ­– rapid-eye-movement (REM, also paradoxical or “dream sleep”) and slow-wave (SW, also non-REM) sleep – but biphasic sleep is widespread, also exists in birds and non-avian reptiles, suggesting a possibly common origin. Studying sleep in the Australian dragon Pogona vitticeps, we have previously described a reptilian homologue of the mammalian claustrum and its role in generating activity patterns characteristic of SW sleep. By recording from the two claustra bilaterally, we then showed that claustrum activity is precisely coordinated across the midline during REM, but not during SW sleep, revealing a fundamental difference in inter-hemispheric coordination during the two main phases of sleep. Exploring the possible identity of circuits that could underlie the generation of the ultradian sleep cycle, we here provide evidence supporting the existence of a central pattern generator (CPG)-type circuit driving the regular alternation between SW and REM sleep. Specifically, exploiting the the extreme regularity and short duration of the Pogona sleep cycle, we reveal two hallmarks of CPG circuits: (1) phase-resetting in response to a phasic input, in conjunction with a clear phase dependence of the effectiveness of this perturbation in causing a phase delay or advance, respectively, and (2) entrainment of an identical rhythm in the awake state, in response to a regular sensory drive whose statistics match those of the natural sleep rhythm.