Radiation-curable acrylates are prepared by a process in which the hydroxy compound is reacted with acrylic acid or methacrylic acid in a first stage and, in a second stage, the reaction product of the first stage is reacted with an epoxide compound in the presence of, as a catalyst, a quaternary ammonium or phosphonium compound of the general formula ##STR1## where X.sup.- is an opposite ion and R.sup.1 to R.sup.4 independently of one another are each C.sub.1 -C.sub.18 -alkyl which may be substituted by one or two phenyl groups or are each C.sub.6 -C.sub.12 -aryl which may be substituted by one or two C.sub.1 -C.sub.6 -alkyl groups.