A model of the chemoreceptor mediated control of breathing is analysed. Hypoxia is simulated as low equilibrium arterial oxygen both at altitude and at sea level. Conditions for stable and unstable equilibria are examined. Transition to instability leads to periodic breathing and the model predicts that this can cause arterial oxygen to oscillate asymmetrically about the equilibrium in some cases, causing the average to rise. Periodic forcing functions have been applied to cerebral blood flow with the same effect on arterial oxygen. Such asymmetric oscillations leading to enhanced oxygenation have been observed in pulse oxymeter recordings from elderly postoperative patients. This may be important in interpreting studies of unstable breathing patterns and their possible relation to morbidity or mortality in infants (e.g. SIDS) and in the elderly (e.g. sleep apnoea, postoperative hypoxia). Periodic breathing could act as a protective adaptation to counteract pre-existing hypoxia.