In the presence of (1) an oxidation catalyst comprising a crystalline complex of manganese with an N,N′-disalicylidenediamine (e.g. N,N′-disalicylidene C2-8 alkylenediamines and N,N′-disalicylidene C6-12 arylenediamines), or (2) an oxidation catalyst comprising the above complex and a basic nitrogen-containing compound, a substrate (e.g., &bgr;-isophorone or a derivative thereof) is oxidized with molecular oxygen to produce a corresponding oxide (e.g., ketoisophorone). Ketoisophorone can be obtained from &bgr;-isophorone with high conversion and high selectivity.