An integral polyether-sulfone membrane with a pore system open at the outer boundaries is in the form of flat films, tubular films or hollow fibers having a maximum pore diameter of 0.02 mu m to 2 mu m. The pore system is cellular throughout with cells having polyhedrally symmetrical boundaries. The cells are arranged asymmetrically from one surface of the membrane to the other, the asymmetry factor AF relative to the maximum pore diameter being 0.01 to 2.0. The ratio of the maximum mean free path length of the flow path to the diameter of the largest pore is greater than 3. The cell size changes steadily from one surface to the other surface. The membrane is produced by dissolving 12 to 35% by weight, relative to the total solution, of polyethersulfone in a mixture of 15 to 65% by weight of epsilon -caprolactam, 0 to 85% by weight of latent solvent, 0 to 15% by weight of thickener and 0 to 50% by weight of non-solvent, and if appropriate up to 1% by weight of auxiliaries, forming the solution into flat films, tubular films or hollow fibers (the latter preferably with the aid of an internal fluid), and transformation into the solid phase and removal of the mixture forming the solvent. The membrane may be used for ultrafiltration and microfiltration.
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