Sleep is known to occur in most, if not all, animals studied thus far. Recent studies demonstrate the presence of sleep in flatworms and jellyfish, suggesting that this behaviour evolved early in the evolution of animals. Sharks are the earliest known extant, jawed vertebrates and may play an important role in understanding the evolutionary history of sleep in vertebrates, and yet, it is unknown whether they sleep. The Port Jackson (Heterodontus portusjacksoni) and draughtsboard (Cephaloscyllium isabellum) sharks are both benthic, buccal pumping species and remain motionless for extended periods of time. Whether these periods of prolonged inactivity represent sleep or quiet wakefulness is unknown. A key criterion for separating sleep from other quiescent states is an increased arousal threshold. We show here that inactive sharks of both species require significantly higher levels of electric stimulation before they show a visible response. Sharks deprived of rest, however, show no significant compensatory increase in restfulness during their normal active period following enforced swimming. Nonetheless, increased arousal thresholds in inactive animals suggest that these two species of shark sleep - the first such demonstration for members of this group of vertebrates. Further research, including electrophysiological studies, on these and other sharks, is required for a comprehensive understanding of sleep in cartilaginous fishes.