Abstract: A multilayer membrane for separating gas mixtures includes a polymer supporting membrane with a voids volume of more than 50% and a coating of two or more separating layers made of two or more different polymers. A hollow capillary serving as the supporting membrane is guided through the central bore of a spinneret. The spinneret has one or several concentric annular slits and/or annular grooves, through each of which a solution of one of the polymers forming the separating layers is applied to the supporting membrane. The spinneret terminates in a sealed chamber in which the solvent or solvents of the polymer solutions is/are evaporated and removed. The coated supporting membrane is drawn out of the chamber and wound up, possibly following aftertreatment with heat and/or liquids.