Described is a method for producing covalently and/or ionically cross-linked blend membranes from a halomethylated polymer, a polymer comprising tertiary N-basic groups, preferably polybenzimidazole, and, optionally, a polymer comprising cation exchanger groups such as sulfonic acid groups or phosphonic acid groups. The membranes can be tailor-made in respect of the properties thereof and are suitable, for example, for use as cation exchanger membranes or anion exchanger membranes in low-temperature fuel cells or low-temperature electrolysis or in redox flow batteries, or—when doped with proton conductors such as phosphoric acid or phosphonic acid—for use in medium-temperature fuel cells or medium-temperature electrolysis.