Cyclohexyl hydroperoxide containing reaction mixtures obtained by oxidation of cyclohexane with molecular oxygen or molecular oxygen containing gases in the liquid phase at from 130.degree. to 200.degree. C. and under from 5 to 125 bar are worked up by reaction with cycloolefins at elevated temperature in the presence of catalysts to react cyclohexyl hydroperoxide with cyclohexene at elevated temperatures in the presence of cyclohexene-soluble compounds of transition metals of groups 4 or 5 or 6 of the periodic table or of one or more cyclohexane-insoluble compounds of a transition metal of group 4 or 5 or 6, or in the presence of selenium, tellurium or a boride, and the resulting cyclohexene oxide at elevated temperatures to cyclohexanol in the presence of hydrogenation catalysts.