Aqueous alkenylsuccinic anhydride-containing polymer dispersions which are obtainable by miniemulsion polymerization of hydrophobic monoethylenically unsaturated monomers in the presence of alkenylsuccinic anhydrides, processes for the preparation of such polymer dispersions by polymerizing hydrophobic monomers by a miniemulsion polymerization method in the presence of at least one alkenylsuccinic anhydride and, if appropriate, an alkyldiketene, and use of the resulting aqueous alkenylsuccinic anhydride-containing polymer dispersions as engine and surface sizes for paper and for imparting water repellency to leather, natural and/or synthetic fibers and textiles.