The invention relates to cross-linkable vinylester-copolymers obtained by means of radically initiated polymerisation of a) one or more vinyl esters and b) one or more ethylenically unsaturated, epoxy functional monomers, and by a subsequent reaction that is analogous to polymerisation of the thus obtained base polymers with one or more ethylenically unsaturated acids g), such that at least one ethylenically unsaturated, polymerizable group is introduced into each base polymer. Said invention is characterised in that the cross-linkable vinylester-copolymers have molecular weights of Mn of ≧6.500 g/mol.