Pyrrolidonyl-containing polyesters and polyamides I to III ##STR1## where R, X, A and Z are defined herein, are suitable as film formers and conditioners in hair-cosmetic formulations, for stabilizing hydrogen-peroxide in aqueous solution, for complexing iodine, as tablet binders and as a constituent of film coatings in pharmaceutical preparations, for enzyme and bleach stabilization in detergent formulations, as an auxiliary in the production and finishing of textiles, as a solubilizer and protective colloid in the preparation and stabilization of polymer dispersions, and as an adhesive raw material.