The oxygenator membrane for oxygen and carbon dioxide exchange has a very low diffusion resistance, whereby the direct contact between gas and blood as in bubble oxygenators or in pore membrane oxygenators is avoided. This is achieved by using a highly porous membrane which is sealed by a very thin layer of polysiloxane (0.1 microns) on one side or by filling the pores with a blood substitute liquid such as fluorocarbons or physiological saline solution. The oxygenator membrane can also be used for germproof shielding and ventilation in clinical areas such as operating theatres or incubators.