The invention relates to a method for producing a mixture of alcohols/ketones by decomposing an alkyl hydroperoxide, particularly to a method for producing a cyclohexanol/cyclohexanone by decomposing cyclohexyl hydroperoxide in the presence of a heterogeneous catalyst. According to the invention, the reaction is carried out in the presence of a heterogeneous catalyst containing an organometallic segment fixed on the surface of a porous solid compound such as silicon. The organometallic segment can be formula (I).