The present invention relates to a continuous method for oxidizing saturated cyclic hydrocarbons by oxygen to obtain a mixture of hydroperoxides, alcohols and ketones. It relates more particularly to a method for oxidizing cyclohexane in a column forming a bubble reactor, for the formation of cyclohexyl hydroperoxide, cyclohexanol and cyclohexanone. According to the invention, the column may be supplied with oxygen-enriched air, while meeting the maximum oxygen concentration requirements in the headspace of the reactor to avoid any risk of explosion.