A process for preparing binders containing allophanate groups which contain, at the oxygen atom of the allophanate group that is bonded via two single bonds, organic radicals with activated groups capable of participating in a polymerization reaction with ethylenically unsaturated compounds on exposure to actinic radiation; the process includes reacting A) one or more compounds containing uretdione groups with B) one or more OH-functional compounds which contain groups capable of participating in a polymerization reaction with ethylenically unsaturated compounds on exposure to actinic radiation, and C) optionally further NCO-reactive compounds, and D) in the presence of one or more compounds containing phenoxide groups, as catalysts. The binders can be used in preparing coatings, coating materials, coating compositions, adhesives, printing inks, casting resins, dental compounds, sizes, photoresists, stereolithography systems, resins for composite materials and sealants.