PROBLEM TO BE SOLVED: To obtain a cycloalkyl hydroperoxide useful for producing both cycloalkanol and cycloalkanone to be used as e.g. raw materials to produce monomers for polyamide polymers such as nylons, as intermediates for chemicals or as organic solvents, etc. SOLUTION: This compound, a cycloalkyl hydroperoxide, is obtained by contact of a solution containing a cyckoalkane (e.g. cyclopentane), cobalt compound (e.g. cobalt chloride) and N-hydroxydicarboxyimide (e.g. N- hydroxyphthalimide) with molecular oxygen pref. at 100-180 deg.C under a pressure of 1-20 atm. Besides, this compound is decomposed into the other objective cycloalkanol and cycloalkanone. These reactions suppress production of byproduct higher-order oxides (adipic acid, etc.) and yields the objective cycloalkyl hydroperoxide, cycloalkanol and cycloalkanone in high reaction rate and selectivity.