The invention relates to a process for preparing cyclohexanedicarboxylic acids or derivatives thereof, such as esters and/or anhydrides, encompassing the reaction of diene/maleic acid anhydride mixtures, in particular of butadiene/maleic acid anhydride mixtures or of mixtures of maleic acid anhydrides and C5-dienes to give alkyl-substituted or unsubstituted cyclohexenedicarboxylic acid anhydrides in the condensed phase, ester formation, and then hydrogenation to give the corresponding cyclohexanedicarboxylic acid derivative, and also to the use of the cyclohexanedicarboxylic acids or derivatives thereof prepared according to the invention as plasticizers for plastics.