Disclosed is a process for the preparation of hydroperoxides comprising liquid-phase oxidizing an aromatic compound having a secondary alkyl group with molecular oxygen in the presence of a basic aqueous solution and a copper compound catalyst, wherein an aqueous solution containing (A) cupric carbonate and (B) an alkali metal carbonate and/or an alkali metal bicarbonate is prepared outside the oxidation system and this aqueous solution is supplied to the oxidation system.According to the process, even under basic conditions, inactivation of the catalyst owing to precipitation is prevented, and the intended aromatic hydroperoxide can be obtained at a high oxidation speed.