Abstract: A process for the conversion of a hydrocarbon fraction comprising a step a) for treating a hydrocarbon charge in the presence of hydrogen in at least one reactor containing at least one hydrodesulphurisation catalyst in a fixed bed under conditions that make it possible to obtain a liquid effluent with a reduced sulphur content, a step b) for treating at least a part of the liquid effluent originating from step a) in the presence of hydrogen in at least one three-phase reactor, containing at least one hydrotreatment catalyst in a boiling bed, operating with an ascending stream of liquid and gas, said reactor comprising at least one means of withdrawing the catalyst from said reactor situated near the bottom of the reactor and at least one means of making up fresh catalyst in said reactor situated near the top of said reactor, and a step c) in which at least part of the product obtained in step b) is passed to a distillation zone from which are recovered a gas fraction, a motor fuel fraction of the petrol type