A novel scheme for extracorporeal oxygenation and/or warming of blood is proposed. It uses a fluorocarbon vapor so premixed with oxygen gas that the saturation temperature of the former is reduced to or below 41°C, the highest temperature permissible for the human blood. The gas/vapor mixture is bubbled directly into the venous blood, resulting in the condensation of the fluorocarbon. The fluorocarbon condensate forms a liquid membrane spread over the surface of each bubble, which prevents the direct contact of blood with gaseous oxygen from occurring and causing blood hemolysis and denaturation of proteins in the blood, but allows the oxygen as well as the latent heat of condensation to diffuse into the blood. The dependencies of blood warming on some operational parameters such as the fluorocarbon-to-blood flow-rate ratio and the oxygen concentration in the mixture have been predicted. The oxygenation of water, a substitute for the blood, has also been examined experimentally.