Layer structure comprising at least one primer layer obtainable from a polyacrylate primer, characterized in that the polyacrylate primer is in the form of an aqueous polymer dispersion, where this aqueous polymer dispersion contains water-dispersed polymer particles and is producible by free-radical polymerization of monomers comprising a) at least 50 percent by weight, based on the total amount of monomers a) to d), of at least one monomer selected from the group consisting of C 1 - to C 20 -alkyl acrylates, C 1 - to C 20 -alkyl methacrylates, vinyl esters of carboxylic acids containing up to 20 carbon atoms, vinylaromatics having up to 20 carbon atoms, vinyl halides, vinyl ethers of alcohols containing 1 to 10 carbon atoms, aliphatic hydrocarbons having 2 to 8 carbon atoms and one or two double bonds, and mixtures of these monomers, and b) at least 0.1 percent by weight, based on the total amount of monomers a) to d), of at least one monomer having at least one acid group and mixtures of these monomers, and c) at least 0.1 to 5 percent by weight, based on the total amount of monomers a) to d), of at least one ethylenically unsaturated compound having at least one functional group selected from keto groups and aldehyde groups, where the aqueous polymer dispersion, in addition to the water-dispersed polymer particles, contains at least one compound AH having at least two functional groups that can enter into a crosslinking reaction with the keto groups or with the aldehyde groups, where the molar ratio of the groups in compound AH that are reactive with keto groups or with aldehyde groups to the keto and aldehyde groups in monomer b) is 1:10 to 2:1; d) optionally further monomers and at least one curable composition based on silane-modified polymers that has been applied to the primer layer, characterized in that the silane-modified polymers have at least one end group of the general formula -A n -R-SiVYZ in which A is a divalent binding group containing at least one heteroatom, R is a divalent hydrocarbyl radical having 1-12 carbon atoms, V, Y, Z are substituents on the silicon atom that are independently C 1 -C 8 -alkyl, C 1 -C 8 -alkoxy or C 1 -C 8 -acyloxy groups, where at least one of the V, Y, Z radicals is a C 1 -C 8 -alkoxy or C 1 -C 8 -acyloxy group, and n is 0 or 1. a) at least 50 percent by weight, based on the total amount of monomers a) to d), of at least one monomer selected from the group consisting of C 1 - to C 20 -alkyl acrylates, C 1 - to C 20 -alkyl methacrylates, vinyl esters of carboxylic acids containing up to 20 carbon atoms, vinylaromatics having up to 20 carbon atoms, vinyl halides, vinyl ethers of alcohols containing 1 to 10 carbon atoms, aliphatic hydrocarbons having 2 to 8 carbon atoms and one or two double bonds, and mixtures of these monomers, and b) at least 0.1 percent by weight, based on the total amount of monomers a) to d), of at least one monomer having at least one acid group and mixtures of these monomers, and c) at least 0.1 to 5 percent by weight, based on the total amount of monomers a) to d), of at least one ethylenically unsaturated compound having at least one functional group selected from keto groups and aldehyde groups, where the aqueous polymer dispersion, in addition to the water-dispersed polymer particles, contains at least one compound AH having at least two functional groups that can enter into a crosslinking reaction with the keto groups or with the aldehyde groups, where the molar ratio of the groups in compound AH that are reactive with keto groups or with aldehyde groups to the keto and aldehyde groups in monomer b) is 1:10 to 2:1; where the aqueous polymer dispersion, in addition to the water-dispersed polymer particles, contains at least one compound AH having at least two functional groups that can enter into a crosslinking reaction with the keto groups or with the aldehyde groups, where the molar ratio of the groups in compound AH that are reactive with keto groups or with aldehyde groups to the keto and aldehyde groups in monomer b) is 1:10 to 2:1; d) optionally further monomers A is a divalent binding group containing at least one heteroatom, R is a divalent hydrocarbyl radical having 1-12 carbon atoms, V, Y, Z are substituents on the silicon atom that are independently C 1 -C 8 -alkyl, C 1 -C 8 -alkoxy or C 1 -C 8 -acyloxy groups, where at least one of the V, Y, Z radicals is a C 1 -C 8 -alkoxy or C 1 -C 8 -acyloxy group, and n is 0 or 1.