Aqueous polymer dispersions comprising a) 50 70% by weight of polymer particles composed of at least two different (co)polymers having glass transition temperatures each above 50.degree. C. and synthesized from at least 80% by weight of at least one principal monomer, 0.1 10% by weight of at least one auxiliary monomer, and 0 3% by weight of at least one crosslinker molecule, the difference in the glass transition temperatures (T.sub.g) of the different polymers being at least 10.degree. C., and b) 30 50% by weight of at least one polyfunctional (meth)acrylate, the dispersion a) being subjected to physical and/or chemical deodorization.