Selected cyclohexane-1,3- and -1,4-dicarboxylic acid esters are described, as is their use as plasticizers in plastics and their preparation by hydrogenation of the corresponding isophthalic or terephthalic esters by bringing one or more of these isophthalic or terephthalic esters into contact with a hydrogen-containing gas in the presence of a catalyst which comprises, as active metal, at least one metal of the 8th transition group of the Periodic Table on its own or together with at least one metal of the 1st or 7th transition group of the Periodic Table, applied to a support, which comprises using a support having micropores.