The search for the neural substrate of a state of consciousness has led to the expectation that there may be neurons which discharge tonically and rhythmically during that state alone. We have now recorded in the cat the first evidence of neurons whose rhythmic discharge is consistent with the hypothesis of a tonically active neural substrate for rapid eye movement (REM) sleep. These neurons, located in the area of gigantocellular and lateral medullary tegmental fields, begin rhythmically discharging simultaneously with the cortical desynchronization at REM sleep onset and cease firing at arousal from REM; they are essentially silent at all other times. Modulations of the discharge rate correlate with the phasic events of REM sleep, such as ataxic breathing and eye movement bursts. In addition, there is a high correlation between their discharge rate and respiratory frequency analyzed on a breath-by-breath basis. The significant rhythmicity of their discharge coupled with high REM selectivity contrasts them with putative REM generators reported by others in the pons and suggests their crucial role in REM generation.