In a process for oxidizing alkylaromatic compounds to the corresponding hydroperoxide, an alkylaromatic compound of general formula (I): ##STR00001## in which R.sup.1 and R.sup.2 each independently represents an alkyl group having from 1 to 4 carbon atoms, provided that R.sup.1 and R.sup.2 may be joined to form a cyclic group having from 4 to 10 carbon atoms, said cyclic group being optionally substituted, and R.sup.3 represents hydrogen, one or more alkyl groups having from 1 to 4 carbon atoms or a cyclohexyl group, 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): ##STR00002## in which R.sup.1, R.sup.2 and R.sup.3 have the same meaning as in formula (I). The hydroperoxide may then be converted into a phenol and a ketone of the general formula R.sup.1COCH.sub.2R.sup.2 (III), in which R.sup.1 and R.sup.2 have the same meaning as in formula (I).