Tungstate is exchanged on a Cl--LDH and converted into peroxo complexes by the action of H2O2. This hydrophilic material is an efficient catalyst for the truly heterogeneous epoxidation of allylic alcohols. The alkaline nature of the LDH suppresses hydrolysis of the epoxides. For simple olefins such as cyclohexene, the use of a Lipophilic LDH, exchanged with WO42- and an organic anion, is more appropriate. In these reactions, the apolar surface provides a suitable micro-environment for epoxide formation with over 90 % selectivity. Finally it is demonstrated that a co-anion such as SO42- favorably influences the selective oxidation by peroxoW, probably through formation of heteronuclear S-W peroxoclusters.