Abstract: An unsaturated (meth) acrylic compound of formula: ##STR1## (X=O, S, NH, NR.sup.3 (R.sup.3 =C.sub.1-12 -alkyl) or O--(CH.sub.2).sub.n (where n=1-16 approximately); R.sup.2 =C.sub.2-20 straight-chain or branched alkyl, monocyclic or polycyclic cycloalkyl or heterocycloalkyl, or alkylaryl hydrocarbon chain, comprising an olefinic double bond in the chain, or at the end of the chain in the case of alkyl or alkylaryl, or an exocyclic or endocyclic olefinic double bond in the case of monocyclic or polycyclic cycloalkyl or heterocycloalkyl; and R.sup.1 =H or C.sub.1-5 -alkyl), is reacted at 10.degree.-60.degree. C. with at least one oxidising compound (hydrogen peroxide) in the presence of at least one catalyst (alkali metal molybdates and tungstates) and in the presence of at least one phase transfer agent and when R.sup.2 =polycyclic cycloalkyl or hetercycloalkyl, an organic peracid or hydrogen peroxide in the presence of at least one heteropolyacid.