Polycocondensates based on aspartic acid which are obtainable by condensing aspartic acid in the presence of polymers containing carboxyl groups, which contain at least 10 mol % of a monoethylenically unsaturated carboxylic acid in copolymerized form and have a molecular weight of at least 300, in the weight ratio from 1,000:1 to 2:1, processes for preparing the polycocondensates and use of the polycocondensates in the form of the free acid groups or in a form neutralized with ammonia, amines, alkali metal or alkaline earth metal bases as an additive to detergents and cleaners, as scale inhibitors or as dispersants for finely divided solids are described.