Abstract: Process for the manufacture of composite plasma membranes with the production of a pore-free impermeable polymer layer on a porous substrate through the plasma polymerization of a gaseous mixture, said gaseous mixture containing a hydrocarbon as the matrix-forming component and a nitrogen-, silicon-, sulphur- or phosphorus-containing inorganic compound as the non-matrix-forming component and an oxygen-containing compound, by means of glow discharge in an electrical alternating field. The pore-free impermeable polymer layer is produced directly on a porous substrate without the use of an impermeable intermediate layer, said porous substrate having a pore diameter of less than 100 nm on the side facing the pore-free polymer layer. The composite plasma membranes are used for separating C.sub.1 -C.sub.3 alkanols from mixtures thereof with other organic liquids using the method of pervaporation.