The functions of slow wave sleep (SWS) and rapid eye movement (REM) sleep, distinct sleep substates present in both mammals and birds, remain unresolved. One approach to gaining insight into their function is to trace the evolution of these states through examining sleep in as many taxonomic groups as possible. The mammalian and avian clades are each composed of two extant groups, i.e., the monotremes (echidna and platypus) and therian (marsupial and eutherian [or placental]) mammals, and Palaeognaths (cassowaries, emus, kiwi, ostriches, rheas, and tinamous) and Neognaths (all other birds) among birds. Previous electrophysiological studies of monotremes and ostriches have identified a unique “mixed” sleep state combining features of SWS and REM sleep unlike the well-delineated sleep states observed in all therian mammals and Neognath birds. In the platypus this state is characterized by periods of REM sleep-related myoclonic twitching, relaxed skeletal musculature, and rapid eye movements, occurring in conjunction with SWS-related slow waves in the forebrain electroencephalogram (EEG). A similar mixed state was also observed in ostriches; although in addition to occurring during periods with EEG slow waves, reduced muscle tone and rapid eye movements also occurred in conjunction with EEG activation, a pattern typical of REM sleep in Neognath birds. Collectively, these studies suggested that REM sleep occurring exclusively as an integrated state with forebrain activation might have evolved independently in the therian and Neognath lineages. To test this hypothesis, we examined sleep in the elegant crested tinamou (Eudromia elegans), a small Palaeognath bird that more closely resembles Neognath birds in size and their ability to fly. A 24-h period was scored for sleep state based on electrophysiology and behavior. Unlike ostriches, but like all of the Neognath birds examined, all indicators of REM sleep usually occurred in conjunction with forebrain activation in tinamous. The absence of a mixed REM sleep state in tinamous calls into question the idea that this state is primitive among Palaeognath birds and therefore birds in general.