Disclosed in a method for producing a mixture containing cycloalkanone and/or cycloalkanol which comprises oxidizing a cycloalkane with molecular oxygen to a cycloalkyl hydroperoxide represented by the formula (1): ##STR1## (wherein m represents an integer of 4.ltoreq.m.ltoreq.11) and decomposing the cycloalkyl hydroperoxide to obtain a mixture containing cycloalkanone and/or cycloalkanol, wherein the oxidation of the cycloalkane with molecular oxygen and/or the decomposition of the cycloalkyl hydroperoxide are carried out in the presence of a catalyst composition comprising at least one metallic salt represented by the formula (2):MX.sub.n (2)(wherein M represent Co, Mn, Cr or Fe, X represents an anionic ligand and n represents 2 or 3) and at least one compound represented by the formula (3): ##STR2## (wherein R.sup.1, R.sup.2, R.sup.3 and R.sup.4 independently represent hydrogen or a lower alkyl group) and/or a catalyst composition comprising at least one metal complex represented by the formula (4): ##STR3## (wherein M represents Co, Mn, Cr or Fe, X represents an anionic ligand, R.sup.1, R.sup.2, R.sup.3 and R.sup.4 independently represent hydrogen or a lower alkyl group, p is 1 or 2 and q is 0, 1 or 2).Advantages of the method are higher conversion of cycloalkyl hydroperoxide, higher yields of cycloalkanone and cycloalkanol and higher production ratio of cycloalkanone.