A process for preparing salts of polyaspartic acid by treating polycondensates in aqueous medium with bases, employing at least 0.7 equivalent of an alkali metal and/or alkaline earth metal base per mole of the aspartimide, aspartic acid and/or aspartamide units present in the polycondensates, and the bases being added within from 30 min to 20 hours to an aqueous suspension of polycondensates of aspartic acid which has been heated to 40.degree.-140.degree. C., and the reaction mixture being allowed to react further where appropriate, and the use of alkali metal and/or alkaline earth metal salts of polyaspartic acids obtainable by treating polycondensates of aspartic acid in aqueous medium with more than 1 equivalent of an alkali metal and/or alkaline earth metal base, with the molecular weight of the polycondensates being reduced, as additive to detergents and cleaners.