A process and the use of a process for desulphurizing a hydrocarbon feed is described which comprises at least one of the following steps: A a step for selective hydrogenation of diolefins present in said initial hydrocarbon feed, in the presence of a catalyst comprising a metal from group VIII of the periodic table on an inert support based on metal oxides, in the presence of a quantity of hydrogen which is in excess with respect to the stoichiometric value necessary for hydrogenating all of said diolefins, the mole ratio between the hydrogen and the diolefins being in the range 1 to 5; b) Extraction, using an appropriate solvent, of said hydrogenated fraction to obtain at least two cuts including: a raffinate comprising the majority of the olefins, paraffins and naphthenes and a reduced quantity of sulphur-containing compounds contained in the initial feed; a heavy fraction containing the heavy aromatic hydrocarbons and the majority of the sulphur-containing compounds contained in the initial feed; C a step for regenerating the solvent by distillation; at least two of steps A, B and C being carried out jointly.