We have conducted the first study of sleep in the platypus Ornithorhynchus anatinus. Periods of quiet sleep, characterized by raised arousal thresholds, elevated electroencephalogram amplitude and motor and autonomic quiescence, occupied 6–8h/day. The platypus also had rapid eye movement sleep as defined by atonia with rapid eye movements, twitching and the electrocardiogram pattern of rapid eye movement. However, this state occurred while the electroencephalogram was moderate or high in voltage, as in non-rapid eye movement sleep in adult and marsupial mammals. This suggests that the low-voltage electroencephalogram is a more recently evolved feature of mammalian rapid eye movement sleep. Rapid eye movement sleep occupied 5.8–8h/day in the platypus, more than in any other animal. Our findings indicate that rapid eye movement sleep may have been present in large amounts in the first mammals and suggest that it may have evolved in pre-mammalian reptiles.