The present invention relates to a process for preparing radiation-curing binders containing allophanate groups by reacting at temperatures of ≦130° C. A) one or more compounds containing uretdione groups with B) one or more OH-functional compounds which contain groups which react, with polymerization, with ethylenically unsaturated compounds on exposure to actinic radiation, (radiation-curing groups), C) optionally NCO-reactive compounds other than B), in the presence of D) a catalyst containing at least one tetrasubstituted ammonium or phosphonium salt of an aliphatic or cycloaliphatic carboxylic acid, to form allophanate groups by opening the uretdione ring. The present invention also relates to the binders obtained by the process of the invention.