In the decerebrate eat the i.v. injection of an anticholinesterase leads to the appearance of a typical pattern of oculomotor activity, which differs from that occurring during physiological sleep in so far as it consists quite exclusively of bursts of REM [rapid eye movement] which appear at regular intervals. Lesion experiments unit recordings show that these bursts of REM depend in particular upon rhythmic discharges of the vestibular nuclear neurons. The underlying anatomical structures responsible for these bursts of REM are the vestibular nuclei, the oculomotor nuclei and the oculo-orbital system. This mechanism is under the influence of cholinergic reticular neurons which generate the oculomotor rhythm. The existence of a self-excitatory cholinergic system is postulated, located in the pontine reticular formation, whose steady discharge impinges upon an oscillatory neuronal system located in the dorso-lateral pontine tegmentum, which transforms the tonic input into a sinusoidal final output. The periodic increases in the discharge frequency of this oscillatory system trigger a fast phase generator acting on the different components of the REM system, and the behavior of each component follows a 1st-order differential equation. The state of excitation of the components of the system is defined as proportional to frequency of nerve impulses. Assuming ipsilateral and crossed connections, a pattern of oculomotor activity is obtained that simulates the experimental oculomotor output fairly well. The repetition of the eye jerks is described by a Fourier series. The model proposed may be taken as a 1st approach in describing the generation mechanism of REM, and as a theoretical guide to jew experimental researches and the development of other more realistic models.