Adequate oxygenation of potentially transplantable tissues must be maintained in patients in a state of cerebral death. An analysis of the relationship between oxygen consumption and arterial oxygen supply shows that proven tissue hypoxia occurs associated with high lactate in almost all patients in a state of cerebral death, even before haemodynamic parameters (blood pressure, heart rate) reach alarming levels. This tissue hypoxia, which exists even though arterial supply remains high, would suggest that there is a defect in peripheral oxygen extraction during the state of cerebral death. Intensive units should take this into account when maintaining these patients.