The use of an aqueous polymer composition as a binder for fibrous or granular substrates, the aqueous polymer composition being obtainable by free radical initiated emulsion polymerization of a monomer mixture M in an aqueous medium in the presence of a polymer A, the polymer A being composed of a) from 80 to 100% by weight of at least one ethylenically unsaturated mono- and/or dicarboxylic acid [monomers A1] and b) from 0 to 20% by weight of at least one further ethylenically unsaturated monomer which differs from the monomers A1 [monomers A2], incorporated in the form of polymerized units, and the monomer mixture M being composed of i) from 0.01 to 10% by weight of at least one ethylenically unsaturated monomer M1 which comprises at least one epoxide group and/or at least one hydroxyalkyl group, and ii) from 90 to 99.99% by weight of at least one further ethylenically unsaturated monomer M2 which differs from the monomers M1, and those monomer mixtures which comprise - from 0.1 to 5% by weight of at least one α,β-monoethylenically unsaturated mono- and/or dicarboxylic acid having 3 to 6 carbon atoms and/or the amide thereof and - from 50 to 99.9% by weight of at least one ester of acrylic and/or methacrylic acid with alkanols having 1 to 12 carbon atoms, or - from 0.1 to 5% by weight of at least one α,β-monoethylenically unsaturated mono- and/or dicarboxylic acid having 3 to 6 carbon atoms and/or the amide thereof and - from 50 to 99.9% by weight of styrene and/or butadiene, or - from 0.1 to 5% by weight of at least one α,β-monoethylenically unsaturated mono- and/or dicarboxylic acid having 3 to 6 carbon atoms and/or the amide thereof and - from 50 to 99.9% by weight of vinyl chloride and/or vinylidene chloride, or - from 0.1 to 5% by weight of at least one α,β-monoethylenically unsaturated mono- and/or dicarboxylic acid having 3 to 6 carbon atoms and/or the amide thereof and - from 40 to 99.9% by weight of vinyl acetate, vinyl propionate and/or ethylene being used as monomers M2. a) from 80 to 100% by weight of at least one ethylenically unsaturated mono- and/or dicarboxylic acid [monomers A1] and b) from 0 to 20% by weight of at least one further ethylenically unsaturated monomer which differs from the monomers A1 [monomers A2], incorporated in the form of polymerized units, i) from 0.01 to 10% by weight of at least one ethylenically unsaturated monomer M1 which comprises at least one epoxide group and/or at least one hydroxyalkyl group, and ii) from 90 to 99.99% by weight of at least one further ethylenically unsaturated monomer M2 which differs from the monomers M1, - from 0.1 to 5% by weight of at least one α,β-monoethylenically unsaturated mono- and/or dicarboxylic acid having 3 to 6 carbon atoms and/or the amide thereof and - from 50 to 99.9% by weight of at least one ester of acrylic and/or methacrylic acid with alkanols having 1 to 12 carbon atoms, or - from 0.1 to 5% by weight of at least one α,β-monoethylenically unsaturated mono- and/or dicarboxylic acid having 3 to 6 carbon atoms and/or the amide thereof and - from 50 to 99.9% by weight of styrene and/or butadiene, or - from 0.1 to 5% by weight of at least one α,β-monoethylenically unsaturated mono- and/or dicarboxylic acid having 3 to 6 carbon atoms and/or the amide thereof and - from 50 to 99.9% by weight of vinyl chloride and/or vinylidene chloride, or - from 0.1 to 5% by weight of at least one α,β-monoethylenically unsaturated mono- and/or dicarboxylic acid having 3 to 6 carbon atoms and/or the amide thereof and - from 40 to 99.9% by weight of vinyl acetate, vinyl propionate and/or ethylene