A process for the concomitant production of at least two hydrocarbon cuts with low sulphur contents from a mixture of hydrocarbons having a total sulphur content in the range 30 to 10000 ppm by weight, by a) hydrodesulphurization in the presence of hydrogen and a hydrodesulphurization catalyst; b) separating hydrogen sulphide from the partially desulphurized effluent obtained from a); c) hydrodesulphurization of the partially desulphurized mixture obtained from b) in the presence of hydrogen and a hydrodesulphurization catalyst, the temperature of the second hydrodesulphurization being higher than that of the first hydrodesulphurization; d) fractionating the desulphurized mixture obtained in c) into at least two desulphurized hydrocarbon cuts.