The invention relates to semipermeable membranes with a water absorption capacity of from 4.5 to 11% by weight, preferably from 4.5 to 8% by weight, as measured on approximately 40.mu. thick symmetrical films at room temperature and at 65% relative air humidity, a throughflow of 130 to 200 l/m.sup.2 d for a desalination level of 94.6 to 99.5% and consisting of an aromatic heterocycle-containing copolyamide with a relative viscosity of .gtoreq.1.4, as measured on a 0.5% N-methyl pyrrolidone solution at a temperature of 20.degree. C.