A membrane for fuel cells, which is characterized by a homogeneous absorption and good retention of doping agents, and which guarantees a high mechanical stability at high temperatures when doped. Such membranes consist of at least one polymer, whose nitrogen atoms are chemically bonded to a central atom of a derivative of a polybasic inorganic oxo acid. The membranes are produced from polymer solutions that are devoid of water and oxo acid derivatives, by heating the solution that has been introduced into a membrane mold until a self-supporting membrane has been formed and then by thermally regulating the latter. Inventive fuel cells having a membrane electrode assembly (MEA) that comprises a membrane of the invention and phosphoric acid as the doping agent have, for example, an impedance of 0.5-1 .OMEGA.cm.sup.2 at a measuring frequency of 1000 Hz and at an operating temperature of 160.degree. C. and a gas flow for hydrogen of 170 mL/min and for air of 570 mL/min. They can be used as high-temperature polyelectrolyte membrane fuel cells for a working temperature of up to at least 250.degree. C.