Abstract: Highly selective membranes for the separation of mixtures He/N.sub.2 and O.sub.2 /N.sub.2, which have suitable mechanical properties and high permeability are dislcosed. They consist of a polymeric porous base from poly-2,6-dimethyl-1,4-phenyleneoxide and a polymeric selective layer formed from polyamidoimide of the general formula I, where R= ##STR1## and n=140-220 ##STR2## or from an interpolymeric equimolar complex of PAI-1 with polyvinylpyrrolidone, or from an aromatic polyimide of the general formula II, where X is --O-- or ##STR3## and n=150-230 ##STR4## or of the general formula III, where n=150-240 ##STR5## or from polymeric imides of the general formula IV, where R=H or CH.sub.3 ##STR6## or also from their copolymers with styrene, methyl methacrylate, methyl acrylate, and dimethylaminoethyl methacrylate. A method for the preparation of composite polymeric membranes consists of saturation of the porous base from poly-2,6-dimethyl-1,4-phenyleneoxide with an organic solvent inert to it, e.g. with C.sub.