Aqueous coating compositions comprising at least one polyisocyanate, characterized in that the polyisocyanate is a non-blocked, hydrophilically modified polyisocyanate (A') or a blocked polyisocyanate (A"), at least one polyurethane which contains free-radically polymerizable groups and from 0 to 0.53 mmol/g, of groups containing Zerevitinov-active hydrogen atoms, characterized in that the polyurethane is a reaction product of (a) one or more polyisocyanates one or more hydrophilicizing compounds containing ionic groups and/or groups which can be converted into ionic groups, selected from the group consisting of mono- and dihydroxycarboxylic acids, mono- and diaminocarboxylic acids, mono- and dihydroxysulphonic acids, mono- and diaminosulphonic acids, mono- and dihydroxyphosphonic acids, mono- and diaminophosphonic acids and their salts, an adduct of isophoronediamine (IPDA) and acrylic acid and its alkali metal and/or ammonium salts, the adduct of sodium bisulphite with but-2-ene-1,4-diol, polyethersulphonate, the propoxylated adduct of 2-butenediol and NaHSO 3, and also units which can be converted into cationic groups, such as N-methyldiethanolamine, and/or non-ionic groups, the nonionically hydrophilizing compounds containing polyether groups and isocyanate-reactive groups, one or more compounds containing free-radically polymerizable groups, if desired, one or more polyol compounds having an average molecular weight of from 50 to 500, and a hydroxyl functionality of greater than or equal to 2 and less than or equal to 3, if desired, one or more polyol compounds having an average molecular weight of from 500 to 13000 g/mol, with an average hydroxyl functionality of from 1.5 to 2.5, and if desired, one or more di- or polyamines, an initiator which is capable of initiating a free-radical polymerization. at least one polyisocyanate, characterized in that the polyisocyanate is a non-blocked, hydrophilically modified polyisocyanate (A') or a blocked polyisocyanate (A"), at least one polyurethane which contains free-radically polymerizable groups and from 0 to 0.53 mmol/g, of groups containing Zerevitinov-active hydrogen atoms, characterized in that the polyurethane is a reaction product of (a) one or more polyisocyanates one or more hydrophilicizing compounds containing ionic groups and/or groups which can be converted into ionic groups, selected from the group consisting of mono- and dihydroxycarboxylic acids, mono- and diaminocarboxylic acids, mono- and dihydroxysulphonic acids, mono- and diaminosulphonic acids, mono- and dihydroxyphosphonic acids, mono- and diaminophosphonic acids and their salts, an adduct of isophoronediamine (IPDA) and acrylic acid and its alkali metal and/or ammonium salts, the adduct of sodium bisulphite with but-2-ene-1,4-diol, polyethersulphonate, the propoxylated adduct of 2-butenediol and NaHSO 3, and also units which can be converted into cationic groups, such as N-methyldiethanolamine, and/or non-ionic groups, the nonionically hydrophilizing compounds containing polyether groups and isocyanate-reactive groups, one or more compounds containing free-radically polymerizable groups, if desired, one or more polyol compounds having an average molecular weight of from 50 to 500, and a hydroxyl functionality of greater than or equal to 2 and less than or equal to 3, if desired, one or more polyol compounds having an average molecular weight of from 500 to 13000 g/mol, with an average hydroxyl functionality of from 1.5 to 2.5, and if desired, one or more di- or polyamines, (a) one or more polyisocyanates one or more hydrophilicizing compounds containing ionic groups and/or groups which can be converted into ionic groups, selected from the group consisting of mono- and dihydroxycarboxylic acids, mono- and diaminocarboxylic acids, mono- and dihydroxysulphonic acids, mono- and diaminosulphonic acids, mono- and dihydroxyphosphonic acids, mono- and diaminophosphonic acids and their salts, an adduct of isophoronediamine (IPDA) and acrylic acid and its alkali metal and/or ammonium salts, the adduct of sodium bisulphite with but-2-ene-1,4-diol, polyethersulphonate, the propoxylated adduct of 2-butenediol and NaHSO 3, and also units which can be converted into cationic groups, such as N-methyldiethanolamine, and/or non-ionic groups, the nonionically hydrophilizing compounds containing polyether groups and isocyanate-reactive groups, one or more compounds containing free-radically polymerizable groups, if desired, one or more polyol compounds having an average molecular weight of from 50 to 500, and a hydroxyl functionality of greater than or equal to 2 and less than or equal to 3, if desired, one or more polyol compounds having an average molecular weight of from 500 to 13000 g/mol, with an average hydroxyl functionality of from 1.5 to 2.5, and if desired, one or more di- or polyamines, an initiator which is capable of initiating a free-radical polymerization.