In the transition from NREM to REM sleep, as in other instances of brain activation, a marked increase in cerebral blood flow and glucose uptake is observed, together with a lesser increase in O2 uptake. Brain activation also entails an increase in capillary PO2 and lactate production. The hypothesis of saturation of the oxidative machinery was advanced to explain anaerobic glycolysis and lactate production in the presence of high PO2, but data are available that cannot be explained by this hypothesis: hypoxic spots exist in the brain, augmenting in arterial hypoxia and disappearing in arterial hyperoxia, while tissue [H+] lowers as arterial PO2 increases beyond 100 mmHg. Additional hypotheses are thus required. We suggest that O2 diffusion limitation exists in the brain: microregions lying at mid-distance between capillaries may become hypoxic and partly resort to anaerobic glycolysis. These microregions are thought to enlarge with increasing metabolic rate or arterial hypoxia and give rise to vasodilatatory signals regulating local blood flow. REM sleep time is strongly reduced by hypoxic and increased by hyperoxic atmosphere, in accordance with the existence of an O2 diffusion limitation. Any pathological decrease in arterial PO2 and/or O2 delivery creates a specific risk in REM sleep.