Abstract: The gas-permeable membrane comprises a reinforcing substrate (2) and a continuous layer (1), deposited thereonto, of a polymer based on an organosilicon rubber. The substrate (2) is made of a solid open-pore material. The layer (1) has a thickness of from 2 to 5 .mu.m and partly fills pores (3). The process for the manufacture of the gas-permeable membrane comprises preparation of a 1-20% solution of a polymer based on an organosilicon rubber in a solvent inert relative to the solid porous substrate material and capable of wetting it. The substrate is heated to a temperature by 0.5.degree.-20.degree. C. above the boiling point of the solvent and the polymer solution is sprayed onto the substrate surface in an amount of from 0.5 to 5 mg/cm.sup.2. The blood oxygenator comprises a plurality of rigid gas-permeable membranes (13) positioned one above another in a housing (17).