The present invention provides a process for preparing radiation-curing allophanates having residual monomer contents of less than 0.5% by weight and an NCO content of less than 1% by weight, wherein (A) compounds containing isocyanate groups, (B) hydroxy-functional compounds which contain groups which react, with polymerization, with ethylenically unsaturated compounds on exposure to actinic radiation (radiation-curing groups) and (C) optionally further compounds containing NCO-reactive groups, also optionally in the presence of a catalyst, are used to form NCO-group-containing urethanes having radiation-curing groups, which are subsequently reacted, without further addition of compounds containing isocyanate groups, in the presence of an allophanatization catalyst, the ratio of NCO groups of the compounds from A) to the OH groups of the compounds from B) and, where used, C) being 1.45:1.0 to 1.1:1.0.