A process for the preparation of aqueous polymer dispersions is described, a vinylaromatic compound, such as, for example, styrene, a conjugated aliphatic diene, such as, for example, butadiene, and an ethylenically unsaturated carbonitrile, such as, for example, acrylonitrile, being copolymerized in an aqueous medium. The copolymerization is effected in the presence of a degraded starch and of free radical initiators. At least part of the monomers differing from ethylenically unsaturated carbonitriles are polymerized before the ethylenically unsaturated carbonitriles are added to the polymerization mixture.