Process for the preparation of polymers of aspartic acid by reacting (a) maleic anhydride and (b) ammonia and/or primary or secondary amines without diluent in the (a):(b) molar ratio of 1:0.1 to 1:3 to give monoamides of maleic acid, fumaric acid or their ammonium salts at up to 100.degree. C. and subsequent condensation of the reaction products, with or without compounds capable of cocondensation, at above 100.degree. C. and, where appropriate, hydrolysis of the condensates and use of the polymers as scale inhibitor, as dispersants for pigments and as additive to detergents and cleaners.