A mixture of radiation-curable, water-dispersible polyurethanes, comprising at least one radiation-curable water-dispersible polyurethane, synthesized from at least one polyisocyanate based on aliphatic and/or cycloaliphatic diisocyanate, at least one compound having at least one, preferably just one, group that is reactive toward isocyanate groups, and having at least one free-radically polymerizable C=C double bond, optionally at least one compound having at least two groups that are reactive toward isocyanate groups, that are selected from hydroxyl, mercapto, primary and/or secondary amino groups, having a number-average molar weight Mn of not more than 500 g/mol, optionally at least one compound having at least two groups that are reactive toward isocyanate groups, that are selected from hydroxyl, mercapto, primary and/or secondary amino groups, having a number-average molar weight Mn of more than 500 g/mol, at least one compound having at least one isocyanate-reactive group and at least one dispersive group, optionally at least one compound other than and that has just one group that is reactive toward isocyanate groups, and optionally at least one polyisocyanate other than, the amount of groups in that are reactive toward isocyanate groups being 0 to not more than 10 mol%, based on the sum of the isocyanate groups in and, and the polyurethane containing at least 3 mol/kg of free-radically polymerizable C=C double bonds, and at least one radiation-curable water-dispersible polyurethane, different from and synthesized from at least one di- or polyisocyanate based on aliphatic and/or cycloaliphatic diisocyanate, at least one compound having at least one, preferably just one, group that is reactive toward isocyanate groups, and having at least one free-radically polymerizable C=C double bond, optionally at least one compound having at least two groups that are reactive toward isocyanate groups, that are selected from hydroxyl, mercapto, primary and/or secondary amino groups, having a number-average molar weight Mn of not more than 500 g/mol, obligatorily at least one compound having at least two groups that are reactive toward isocyanate groups, that are selected from hydroxyl, mercapto, primary and/or secondary amino groups, having a number-average molar weight Mn of more than 500 g/mol, at least one compound having at least one isocyanate-reactive group and at least one dispersive group, optionally at least one compound other than and that has just one group that is reactive toward isocyanate groups, and optionally at least one polyisocyanate other than, at least one of the compounds being a polyesterdiol in an amount of groups in that are reactive toward isocyanate groups of more than 10 mol%, based on the sum of the isocyanate groups in and, with a mass ratio: of 5:95 to 95:5, wherein the polyurethane has a glass transition temperature of more than 20°C and the polyurethane has a glass transition temperature of not more than 10°C (to be determined as T g according to the DSC method (Differential Scanning Calorimetry) according to ASTM 3418/82 at a heating rate of 10°C/min) and the compound is a polyisocyanate having at least one moiety selected from the group consisting of isocyanurates, biurets, and allophanates. at least one polyisocyanate based on aliphatic and/or cycloaliphatic diisocyanate, at least one compound having at least one, preferably just one, group that is reactive toward isocyanate groups, and having at least one free-radically polymerizable C=C double bond, optionally at least one compound having at least two groups that are reactive toward isocyanate groups, that are selected from hydroxyl, mercapto, primary and/or secondary amino groups, having a number-average molar weight Mn of not more than 500 g/mol, optionally at least one compound having at least two groups that are reactive toward isocyanate groups, that are selected from hydroxyl, mercapto, primary and/or secondary amino groups, having a number-average molar weight Mn of more than 500 g/mol, at least one compound having at least one isocyanate-reactive group and at least one dispersive group, optionally at least one compound other than and that has just one group that is reactive toward isocyanate groups, and optionally at least one polyisocyanate other than, at least one di- or polyisocyanate based on aliphatic and/or cycloaliphatic diisocyanate, at least one compound having at least one, preferably just one, group that is reactive toward isocyanate groups, and having at least one free-radically polymerizable C=C double bond, optionally at least one compound having at least two groups that are reactive toward isocyanate groups, that are selected from hydroxyl, mercapto, primary and/or secondary amino groups, having a number-average molar weight Mn of not more than 500 g/mol, obligatorily at least one compound having at least two groups that are reactive toward isocyanate groups, that are selected from hydroxyl, mercapto, primary and/or secondary amino groups, having a number-average molar weight Mn of more than 500 g/mol, at least one compound having at least one isocyanate-reactive group and at least one dispersive group, optionally at least one compound other than and that has just one group that is reactive toward isocyanate groups, and optionally at least one polyisocyanate other than,