A procedure for producing hydroquinone from a hydrocarbon mixture obtained as a by-product when producing cumene, by selectively oxidizing tertiary alkylaromatics to form hydroperoxides, by separating the dihydroperoxide of p-diisopropylbenzene from the oxidation product by selective crystallization through cooling, and by decomposing the dihydroperoxide of p-diisopropylbenzene with the aid of an acid catalyst to form the hydroquinone.