Abstract: The invention relates to a semipermeable composite membrane comprising a microporous substrate provided with a semipermeable microporous substrate membrane which is provided, on at least one side, with a water-permeable polymer layer, said polymer layer containing the interfacial-polymerization product of an amine-terminal dendrimer and a compound polymerizing therewith. According to the invention, the amine-terminal dendrimers used, are poly(alkylene imine) dendrimers. These dendrimers preferably have terminal primary and/or secondary amine groups. In particular, use is made of a 1,4-diaminobutane ?4!: (1-azabutylidene).sup.x-4 : propylamine or propyl-N-alkyl-amine, wherein x=4, 8, 16, 32 or 64. Expediently, the compound which polymerizes with the dendrimer is selected from the group consisting of a carboxylic acid or carboxylic acid derivative, a sulphonic acid or sulphonic acid derivative, and an isocyanate compound.