Mammalian sleep is not a homogenous state, and different variables have traditionally been used to distinguish different periods during sleep. Of these variables, eye movement is one of the most paradigmatic, and has been used to differentiate between the so-called rapid eye movement (REM) and non-REM (NREM) sleep periods. Despite this, eye movements during sleep are poorly understood, and the behaviour of the oculomotor system remains almost unknown. In the present work, we recorded binocular eye movements during the sleep-wake cycle of adult cats by the scleral search-coil technique. During alertness, eye movements consisted of conjugated saccades and eye fixations. During NREM sleep, eye movements were slow and mostly unconjugated. The two eyes moved upwardly and in the abducting direction, producing a tonic divergence and elevation of the visual axis. During the transition period between NREM and REM sleep, rapid monocular eye movements of low amplitude in the abducting direction occurred in coincidence with ponto-geniculo-occipital waves. Along REM sleep, the eyes tended to maintain a tonic convergence and depression, broken by high-frequency bursts of complex rapid eye movements. In the horizontal plane, each eye movement in the burst comprised two consecutive movements in opposite directions, which were more evident in the eye that performed the abducting movements. In the vertical plane, rapid eye movements were always upward. Comparisons of the characteristics of eye movements during the sleep-wake cycle reveal the uniqueness of eye movements during sleep, and the noteworthy existence of tonic and phasic phenomena in the oculomotor system, not observed until now.