Good salt rejection and flux characteristics can be obtained with reverse osmosis membranes made from crosslinked, interfacially polymerized aromatic polyamides, particularly poly(arylenepolyamine aromaticpolycarboxylamides) such as poly(phenylenediamine trimesamide). The aromatic polyamides are preferably synthesized directly from an essentially monomeric polyacyl halide (at least tri- or higher in acyl functionality) and an essentially monomeric arylene polyamine with a measurable water solubility. As compared to closely analogous linear polymers, these interfacially polymerized, crosslinked polyamides have a lower % elongation and lower solubility (e.g. in amide solvents). Chlorine resistance characteristics of these polyamides are also good and can be improved by treatment with a chlorinating agent. In the preferred practice of the method for making a reverse osmosis membrane, a porous support layer is coated with the polyamine component (e.g. an aqueous solution of phenylene diamine); the thus-coated support is contacted with the polyacyl halide component (e.g. trimesoyl chloride), thereby initiating the interfacial polymerization in situ on the support; and the resulting product is dried to provide a composite membrane comprising the polyamide laminated to the porous support.