Compositions, in particular cosmetic compositions, comprising a cyclohexane-based compound defined by formula (I): 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.