The use of an aqueous polymer dispersion obtainable by polymerizing a composition 1 of compounds containing at least one ethylenically unsaturated group (monomers) by the method of radical aqueous emulsion polymerization to a conversion of at least 90%, based on the monomer composition 1 to be polymerized (polymerization stage 1), and subsequently, in the presence of the product mixture from polymerization stage 1, polymerizing a composition 2 of compounds containing at least one ethylenically unsaturated group (monomers) by the method of radical aqueous emulsion polymerization (polymerization stage 2), with the proviso that a) composition 1 is such that random copolymerization of composition 1 alone would give a polymer 1 with a glass transition temperature Tg1 > 0°C, b) composition 2 is such that random copolymerization of composition 2 alone would give a polymer 2 with a glass transition temperature Tg2 > 80°C, c) the amount of the difference between Tg1 and Tg2 is at least 50°C, d) further to the monomers of compositions 1 and 2, at least one adhesion monomer, which is different from these monomers and comprises at least one ethylenically unsaturated group and the element nitrogen, is copolymerized in an amount of 0.1% to 10% by weight, based on the total amount of the monomers to be polymerized, e) of the total amount of the adhesion monomers to be copolymerized as per d), 20 to 100 mol% are copolymerized in polymerization stage 1, and f) the amount of the composition i that is accorded the lower limit value Tgi, based on the total amount of the compositions 1 and 2, is 60% to 90% by weight, g) further to the monomers of compositions 1 and 2, at least one monomer which is different from these monomers and is selected from the group consisting of itaconic acid, acetoacetoxyethyl (meth)acrylate (AAEM), and acrylonitrile is copolymerized in an amount of 0.2% to 25% by weight, based on the total amount of the monomers to be polymerized, for coating compositions having improved resistance toward chemicals. a) composition 1 is such that random copolymerization of composition 1 alone would give a polymer 1 with a glass transition temperature Tg1 > 0°C, b) composition 2 is such that random copolymerization of composition 2 alone would give a polymer 2 with a glass transition temperature Tg2 > 80°C, c) the amount of the difference between Tg1 and Tg2 is at least 50°C, d) further to the monomers of compositions 1 and 2, at least one adhesion monomer, which is different from these monomers and comprises at least one ethylenically unsaturated group and the element nitrogen, is copolymerized in an amount of 0.1% to 10% by weight, based on the total amount of the monomers to be polymerized, e) of the total amount of the adhesion monomers to be copolymerized as per d), 20 to 100 mol% are copolymerized in polymerization stage 1, and f) the amount of the composition i that is accorded the lower limit value Tgi, based on the total amount of the compositions 1 and 2, is 60% to 90% by weight, g) further to the monomers of compositions 1 and 2, at least one monomer which is different from these monomers and is selected from the group consisting of itaconic acid, acetoacetoxyethyl (meth)acrylate (AAEM), and acrylonitrile is copolymerized in an amount of 0.2% to 25% by weight, based on the total amount of the monomers to be polymerized, for coating compositions having improved resistance toward chemicals.