A curable aqueous polyurethane dispersion substantially comprises a) at least one compound having two free isocyanate groups, at least one allophanate group and at least one C═C double bond capable of free radical polymerization, a carbonyl group or an oxygen atom in the form of an ether function being bonded directly to the double bond, b) at least one compound having at least one group reactive toward isocyanate groups and having a C═C double bond capable of free-radical polymerization, c) if required, at least one compound having at least two groups reactive towards isocyanate groups and selected from hydroxyl, mercapto, primary and/or secondary amino groups, d) at least one compound having at least one group reactive towards isocyanate groups and having at least one acid group, e) at least one basic compound for neutralizing or partially neutralizing the acid groups of the compounds d), and a thermal initiator and is used for coating substrates.