An acid-doped, single-layer or multilayer polymer membrane comprising at least one layer A of a polymer blend with contains: a) from 0.1 to 99.9% by weight of one or more polymers comprising recurring azole units of the formula 1A and/or 1B: ##STR00001## wherein the radicals Ar, Ar.sup.1, and Ar.sup.2 are tetravalent, divalent or trivalent aromatic or heteroaromatic groups and the radicals X are each and oxygen atom, a sulfur atom or an amino group bearing a hydrogen atom, a 1-20 carbon group, in admixture with b) from 99.9 to 0.1% by weight of a polysulfone containing recurring unit having no sulfonic acid groups.