Process for the preparation of 3,4-epoxyalkane- and/or 4-hydroxy-2-alkene carbonic acids and their esters

3,4-Epoxyalkanoic acids and esters thereof of the general formula I in which R , R , R , R , R denote hydrogen or an acyclic, cyclic or unbranched alkyl or aralkyl radical having 1 to 30 carbon atoms, and/or 4-hydroxy-2-alkenoic acids and esters thereof of the general formula II in which R to R have the meanings given for compounds I are prepared by reacting 3-alkenoic acids or esters thereof of the general formula III in which R to R have the meanings given for compounds I, in the presence of a catalyst with 4-hydroperoxy-2-alkenoic acids or esters thereof of the general formula IV in which R to R have the meanings given for compounds I, at 50 to 150 DEG C and 0.01 to 50 bar.