PURPOSE: To obtain the aimed substance in high yield in a short time, by dissolving a compound of Rh, Pd, Ir, Au, etc., in a reaction solution and carrying out reaction in oxidizing the titled substance in the liquid phase with molecular oxygen to give hydroperoxides and/or carbinols.

CONSTITUTION: At least one metal compound selected from Rh, Pd, Ir and Au is dissolved in a soluble solvent, preferably an aqueous solution of a base to prepare a catalyst solution. The resultant catalyst solution, together with a base and secondary alkyl group-substituted naphthalenes which are a raw material, e.g. diisopropylnaphthalene, is charged into a reactor so that the metal compound may be present in an amount of ≥0.5ppm expressed in terms of the metal to carry out reaction and afford hydroperoxides and/or carbinols, etc. In the reaction, a reaction initiator, e.g. α,α-azobis(cyclohexane-1- carbonitrile), etc., is preferably used. Thereby the amount of the catalyst can be reduced and the oxidation rate can be simultaneously increased.