Cerebral blood flow was estimated on 60 occasions in 15 well infants, 29-34 wk of gestational age, 5-17 days after birth, using 133-Xenon clearance after intravenous injection. The sleep state of the infants was determined by biparietal electroencephalography, clinical observation, and tracings of heart rate and respiration. Blood flow was 22% higher in the 11 estimations made during wakefulness, when compared to the 17 estimations made during quiet sleep. There was no difference between blood flow in active and quiet sleep. Also there was no difference between blood flow during periods of trace alternant and blood flow during periods of continuous electroencephalographic activity. It is suggested that flow-metabolism coupling is present in stable, preterm infants. The absence of an increase in cerebral blood flow during active sleep as compared with quiet sleep suggests that the neurophysiologic and neurometabolic mechanisms of rapid eye movement sleep are not yet fully developed in preterm infants.