PROBLEM TO BE SOLVED: To form an objective oxidation product with a high selectivity by using an oxidation catalyst system consisting of a specified imide compd. and a prim. or sec. alcohol. SOLUTION: The oxidation catalyst system consists of an imide compd. of the formula and a prim. or sec. alcohol as a co-oxidizing agent. In the formula, R and R are mutually the same or different and are each H, a halogen, alkyl, aryl, cycloalkyl, hydroxyl, alkoxy, carboxyl or acyl, R and R may bond to each other to form a double bond or an arom. or nonarom. ring, X is O or hydroxyl and (n) is an integer of 1-3.