A process for reducing the quantity of sulphur present in a hydrocarbon feed such as a gasoline or a gas oil, comprises: d) bringing said feed containing sulphur-containing compounds into contact with an adsorbent having a selectivity for sulphur-containing compounds under conditions for producing, at the outlet from the contact zone, a desulphurized effluent which is collected, said adsorption being carried out in the liquid phase or in the gas phase; e) gas phase desorption of the sulphur-containing compounds present on said adsorbent using a hydrogen-containing gaseous fluid derived from a hydrodesulphurization zone to obtain a gaseous effluent comprising hydrogen and desorbed sulphur-containing compounds; sending the gaseous effluent from step b) to said hydrodesulphurization zone and desulphurizing it therein.