In a process for oxidizing alkylaromatic compounds to the corresponding hydroperoxide, an alkylaromatic compound of general formula (I): in which R1 and R2 each independently represents an alkyl group having from 1 to 4 carbon atoms, provided that R1 and R2 may be joined to form a cyclic group having from 4 to 10 carbon atoms, said cyclic group being optionally substituted, and R3 represents hydrogen, one or more alkyl groups having from 1 to 4 carbon atoms or a cyclohexyl group, is contacted with oxygen in the presence of an added catalyst comprising tert-butyl hydroperoxide and in the absence of any other catalyst, to produce a hydroperoxide of general formula (II): in which R1, R2 and R3 have the same meaning as in formula (I). The hydroperoxide may then be converted into a phenol and a ketone of the general formula R1COCH2R2 (III), in which R1 and R2 have the same meaning as in formula (I).