Disclosed herein are aqueous polymer compositions, which are obtainable by radical copolymerization in water; a process for producing the aqueous polymer compositions; a method of using the aqueous polymer compositions as an anti-greying additive in washing or laundry; a method of using the aqueous polymer compositions as an anti-greying additive in liquid laundry detergent formulations or gel-type laundry detergent formulations; and a liquid laundry detergent formulation or gel-type laundry detergent formulation, which contains at least one aqueous polymer composition.