Electrolytic membrane comprising an ion-conducting polymer which is fixed in the pores of a porous polyalkene membrane stretched in at least one direction, wherein the polyalkene membrane has a porosity of 30-90% and a mean pore diameter of 0.1 to 5.0 .mu.m. The electrolytic membrane can be manufactured by impregnating the polyalkene with a suitable solution of the ion-conducting polymer at a temperature which is at least 80.degree. C., preferably at least 110.degree. C., and which is not above the melting point of the polyalkene membrane used. The electrolytic membrane is very suitable for use in solid-polymer fuel cells and batteries.