The invention relates to a process for preparing binders which contain 1) allophanate groups, 2) groups that react with ethylenically unsaturated compounds with polymerization on exposure to actinic radiation (radiation-curing groups) and 3) optionally NCO-reactive groups, by reacting at temperatures ≦130° C. A) one or more NCO-functional compounds containing uretdione groups with B) one or more compounds that contain isocyanate-reactive groups and groups that react with ethylenically unsaturated compounds with polymerization on exposure to actinic radiation (radiation-curing groups), and then C) with one or more saturated, hydroxyl-containing compounds other than B), at least one of these compounds having an OH functionality of ≧2, in the presence of D) a catalyst containing one or more ammonium salts or phosphonium salts of aliphatic or cycloaliphatic carboxylic acids, the reaction with compounds C) taking place at least proportionally with the formation of allophanate groups. The present invention also relates to the binders obtained by the process of the invention.