Abstract: A method for producing integral, asymmetric membranes for separating mixtures of gases is disclosed. A membrane forming polymer, a solvent for the polymer, and a swelling agent are mixed to form a pourable liquid mixture; the solvent has a lower boiling point than the other components in the mixture, the polymer is not soluble in the swelling agent, and the swelling agent does not react with the polymer or the solvent. The liquid mixture is spread to form a thin film, the film is exposed to air or an inert gas to form a surface skin by evaporation and is thereafter contacted with a precipitation agent. A preferred integral, asymmetric membrane is produced when the membrane forming polymer is a polyetherimide, the solvent is a halogenated hydrocarbon and the swelling agent is one or more compound selected from the group consisting of an alkyl substituted benzene, an aliphatic carboxylic acid, and a chlorinated hydrocarbon.