The present invention relates to a process for the oxidation, in an inert solvent, of a non-aromatic or non-enonic ethylenic bond or of a non-conjugated cyclic ketones into the corresponding epoxides, respectively lactone, using H.sub.2O.sub.2 as oxidant, a content in water of the reaction medium below 15% w/w and, as sole catalyst, an alkaline or alkaline earth salt or complex.