Abstract: The invention relates to a process for producing a thermoformable polymer/fiber composite using an aqueous dispersion of a polymer P and a fibrous substrate, where the dispersion is obtained by free-radically initiated emulsion polymerization of a monomer composition composed of 5% to 30% by weight of one or more monomers M1 selected from esters of acrylic and/or methacrylic acid with alkanols having 2 to 8 carbon atoms, 70% to 95% by weight of styrene and/or methyl methacrylate (M2), and 0% to 10% by weight of at least one further ethylenically unsaturated compound (M3) which is copolymerizable with monomers M1 and M2, based in each case on the total amount of the monomers M, in an aqueous medium in the presence of a polymer A or a polymer mixture A, where polymer A or polymer mixture A is formed from 40% to 70% by weight of acrylic acid (monomer A1), 30% to 60% by weight of maleic acid and/or maleic anhydride (monomer A2), 0% to 5% by weight of at least one further ethylenically unsaturated compound whic