Sleep is a state of immobility characterized by three key criteria: an increased threshold of arousal, rapid reversal to an alert state and evidence of homeostatic ‘rebound sleep’ in which there is an increase in the time spent in this quiescent state following sleep deprivation. Common European cuttlefish, Sepia officinalis, show states of quiescence during which they meet the last two of these three criteria, yet also show spontaneous bursts of arm and eye movements that accompany rapid changes in chromatophore patterns in the skin. Here, we report that this rapid eye movement sleep-like (REMS-like) state is cyclic in nature. Iterations of the REMS-like state last 2.42±0.22 min (mean±s.e.m.) and alternate with 34.01±1.49 min of the quiescent sleep-like state for durations lasting 176.89±36.71 min. We found clear evidence that this REMS-like state (i) occurs in animals younger than previously reported; (ii) follows an ultradian pattern; (iii) includes intermittent dynamic chromatophore patterning, representing fragments of normal patterning seen in the waking state for a wide range of signaling and camouflage; and (iv) shows variability in the intensity of expression of these skin patterns between and within individuals. These data suggest that cephalopods, which are mollusks with an elaborate brain and complex behavior, possess a sleep-like state that resembles behaviorally the vertebrate REM sleep state, although the exact nature and mechanism of this form of sleep may differ from that of vertebrates.