Compositions, in particular cosmetic compositions, comprising a cyclohexane-based compound defined by formula (I): ##STR00001## wherein: R, which may be identical or different, are each chosen from hydrogen atoms and linear and branched, saturated hydrocarbons comprising 1 to 6 carbon atoms; Y, which may be identical or different, are each chosen from --CO--S--R' groups, --CO--NHR' groups, NH--COR' groups and --S--COR' groups, wherein R', which may be identical or different, are each chosen from hydrogen atoms, aryl groups, optionally substituted with at least one hydrocarbon comprising 1 to 22 carbon atoms, wherein said hydrocarbon is chosen from linear and branched, saturated and unsaturated hydrocarbons, and linear, branched and cyclic, saturated and unsaturated hydrocarbons comprising 1 to 22 carbon atoms, wherein said hydrocarbons may optionally be substituted with at least one group chosen from aryl groups, ester groups, amide groups and urethane groups; wherein said hydrocarbons may optionally comprise at least one hetero atom chosen from O, S and N; and wherein said hydrocarbons may optionally be substituted with at least one entity chosen from fluorine atoms and hydroxyl groups; with the proviso that at least one of said R' comprises at least one unsaturated hydrocarbon. Compounds of formula (I) and their use for structuring a composition, in particular a cosmetic composition.