A process for producing a thermoformable polymer/fiber composite using a fibrous substrate, an organic di- or polyisocyanate compound I and a polymer P, wherein • the fibrous substrate is introduced into a gas stream, then • the fibrous substrate in the gas stream is contacted with an aqueous dispersion of a polymer P having a glass transition temperature Tg and an organic di- or polyisocyanate compound I, then • the fibrous substrate that has been contacted with the aqueous dispersion of the polymer P and the organic di- or polyisocyanate compound I is dried in the gas stream and then deposited, then • the deposited fibrous substrate obtained is converted to a fiber web, and then • the fiber web obtained is consolidated at a temperature ≥ Tg to give a thermoformable polymer/fiber composite, and wherein the aqueous dispersion of the polymer P is effected by free-radically initiated emulsion polymerization of a mixture of ethylenically unsaturated monomers P [monomers P] in an aqueous medium in the presence of a polymer A, wherein the polymer A is formed from a) 80% to 100% by weight of at least one ethylenically unsaturated mono- and/or dicarboxylic acid, called monomers A1, and b) 0% to 20% by weight of at least one further ethylenically unsaturated monomer which differs from the monomers A1 [monomers A2], in copolymerized form, and wherein the monomers P are chosen in terms of type and amount such that the polymer P obtained has a glass transition temperature Tg ≥ 20°C measured according to DIN EN ISO 11357-2, and wherein a fibrous substrate means those particles having a ratio of their longest dimension to their shortest dimension of at least ≥ 5. • the fibrous substrate is introduced into a gas stream, then • the fibrous substrate in the gas stream is contacted with an aqueous dispersion of a polymer P having a glass transition temperature Tg and an organic di- or polyisocyanate compound I, then • the fibrous substrate that has been contacted with the aqueous dispersion of the polymer P and the organic di- or polyisocyanate compound I is dried in the gas stream and then deposited, then • the deposited fibrous substrate obtained is converted to a fiber web, and then • the fiber web obtained is consolidated at a temperature ≥ Tg to give a thermoformable polymer/fiber composite, and wherein the aqueous dispersion of the polymer P is effected by free-radically initiated emulsion polymerization of a mixture of ethylenically unsaturated monomers P [monomers P] in an aqueous medium in the presence of a polymer A, wherein the polymer A is formed from a) 80% to 100% by weight of at least one ethylenically unsaturated mono- and/or dicarboxylic acid, called monomers A1, and b) 0% to 20% by weight of at least one further ethylenically unsaturated monomer which differs from the monomers A1 [monomers A2], in copolymerized form, and wherein the monomers P are chosen in terms of type and amount such that the polymer P obtained has a glass transition temperature Tg ≥ 20°C measured according to DIN EN ISO 11357-2, and wherein a fibrous substrate means those particles having a ratio of their longest dimension to their shortest dimension of at least ≥ 5. and wherein the aqueous dispersion of the polymer P is effected by free-radically initiated emulsion polymerization of a mixture of ethylenically unsaturated monomers P [monomers P] in an aqueous medium in the presence of a polymer A, wherein the polymer A is formed from a) 80% to 100% by weight of at least one ethylenically unsaturated mono- and/or dicarboxylic acid, called monomers A1, and b) 0% to 20% by weight of at least one further ethylenically unsaturated monomer which differs from the monomers A1 [monomers A2], in copolymerized form, a) 80% to 100% by weight of at least one ethylenically unsaturated mono- and/or dicarboxylic acid, called monomers A1, and b) 0% to 20% by weight of at least one further ethylenically unsaturated monomer which differs from the monomers A1 [monomers A2], in copolymerized form, and wherein the monomers P are chosen in terms of type and amount such that the polymer P obtained has a glass transition temperature Tg ≥ 20°C measured according to DIN EN ISO 11357-2, and wherein a fibrous substrate means those particles having a ratio of their longest dimension to their shortest dimension of at least ≥ 5.