Described is a method of producing polymers of aspartic acid by reacting (a) maleic acid anhydride and (b) ammonia and/or primary or secondary amines essentially in the molar ratio (a):(b) of 1:0.1 to 1:3 to give half-amides of maleic acid or fumaric acid, or their ammonium salts, at temperatures of up to 100 DEG C and subsequently condensing the reaction products with each other, optionally also with compounds capable of condensing with them, at temperatures above 100 DEG C and optionally hydrolysing the condensation products. Also described is the use of the polymers thus produced as scale inhibitors, pigment dispersants and additives to washing and cleaning agents.