Selective, water-permeable membranes for reverse osmosis and nanofiltration are prepared by interfacially polymerizing on a microporous support an essentially monomeric bipiperidine reactant, and an essentially monomeric amine-reactive polyfunctional aromatic or cycloaliphatic acyl halide having on the average at least about 2 acyl halide groups per reactant molecule. The polymerization is optionally carried out in the presence of a monomeric amine salt, which can increase the flux rate of the resulting membrane.