A process for cooxidizing organic compounds which comprises, in the presence of an imide compound such as N-hydroxyphthalimide, oxidizing with molecular oxygen a compound (A) which is selected from among (A1) compounds having nonaromatic ethylenic linkage and (A2) ketones or alcohols corresponding to the ketones and a compound (B) which can be oxidized by the above imide compound with oxygen and is different from the above compound (A). As the compound (B), use can be made of (a) primary or secondary alcohols (benzhydrol, cyclohexanol, etc.), and (b) compounds having a carbon-hydrogen bond adjacent to an unsaturated bond (tetralin, ethylbenzene, etc.). Use of this process makes it possible to obtain the corresponding epoxy compounds from (A1) compounds having nonaromatic ethylenic linkage, and the corresponding esters or lactones from (A2) ketones or alcohols corresponding to the ketones, each at a high yield.