A semipermeable membrane made of a polyaryl ether sulfone comprised of recurring units represented by the general formula (I): ##STR1## wherein X, X', X" and X"' are non-dissociative substituents, and l, m, n and o are integers of from 0 to 4. The membrane, which is composed of a single continuous polymer phase, has pores of a diameter increasing progressively and continuously from the surface layers to the center portion thereof.The membrane is prepared by the process wherein:the polyaryl ether sulfone is dissolved in a mixed solution to form a dope of the polyaryl ether sulfone;the polyaryl ether sulfone dope is extruded to form a fiber or film and, then;both sides of the fiber or film are contacted with a liquid miscible with the mixed solvent but incapable of dissolving the polyaryl ether sulfone to remove substantially all the mixed solvent from the fiber or film.