Sleep has been observed in several invertebrate species, but its presence in marine invertebrates is relatively unexplored. Rapid-eye-movement (REM) sleep has only been observed in vertebrates. We investigated whether the cuttlefish Sepia officinalis displays sleep-like states. We find that cuttlefish exhibit frequent quiescent periods that are homeostatically regulated, satisfying two criteria for sleep. In addition, cuttlefish transiently display a quiescent state with rapid eye movements, changes in body coloration and twitching of the arms, that is possibly analogous to REM sleep. Our findings thus suggest that at least two different sleep-like states may exist in Sepia officinalis.