During sleep our brain switches between two starkly different brain states - slow wave sleep (SWS) and rapid eye movement (REM) sleep. While this two-state sleep pattern is abundant across birds and mammals, its existence in other vertebrates is not universally accepted, its evolutionary emergence is unclear and it is undetermined whether it is a fundamental property of vertebrate brains or an adaptation specific to homeotherms. To address these questions, we conducted electrophysiological recordings in the Agamid lizard, Laudakia vulgaris during sleep. We found clear signatures of two-state sleep that resemble the mammalian and avian sleep patterns. These states switched periodically throughout the night with a cycle of ~90 seconds and were remarkably similar to the states previously reported in Pogona vitticeps. Interestingly, in contrast to the high temperature sensitivity of mammalian states, state switches were robust to large variations in temperature. We also found that breathing rate, micro-movements and eye movements were locked to the REM state as they are in mammals. Collectively, these findings suggest that two-state sleep is abundant across the agamid family, shares physiological similarity to mammalian sleep, and can be maintain in poikilothems, increasing the probability that it existed in the cold-blooded ancestor of amniotes.