A process for the desulphurization of a gasoline containing sulphur-containing compounds, olefins and diolefins, the process comprising at least the following steps: a) fractionating the gasoline in order to recover a light gasoline cut LCN and a first heavy gasoline cut HCN; b) carrying out a first step for desulphurization of the first heavy gasoline cut HCN in the presence of a hydrodesulphurization catalyst and hydrogen, at a temperature in the range 160°C to 450°C, at a pressure in the range 0.5 to 8 MPa, with a liquid velocity in the range 0.5 to 20 h -1 and with a ratio between the flow rate of hydrogen, expressed in normal m 3 per hour, and the flow rate of feed to be treated, expressed in m 3 per hour under standard conditions, in the range 50 Nm 3 /m 3 to 1000 Nm 3 /m 3 in a manner such as to produce a first desulphurization effluent; c) partially condensing the first desulphurization effluent obtained from step b) in a manner such as to produce a gaseous phase essentially constituted by hydrogen and H 2 S and a liquid hydrocarbon phase HCN comprising dissolved H 2 S; d) separating the liquid hydrocarbon phase HCN into an intermediate gasoline cut MCN and a second heavy gasoline cut HHCN; e) carrying out a second step for desulphurization of the second heavy gasoline cut HHCN in the presence of a hydrodesulphurization catalyst and hydrogen, at a temperature in the range 160°C to 450°C, at a pressure in the range 0.5 to 8 MPa, with a liquid velocity in the range 0.5 to 20 h -1 and with a ratio between the flow rate of hydrogen, expressed in normal m 3 per hour, and the flow rate of feed to be treated, expressed in m 3 per hour under standard conditions, in the range 50 Nm 3 /m 3 to 1000 Nm 3 /m 3 in a manner such as to produce a desulphurized second heavy gasoline cut HHCN, the process comprising: • a step c') in which the dissolved H 2 S of the liquid hydrocarbon phase HCN obtained from step c) is separated in order to produce a liquid hydrocarbon phase HCN with a low dissolved H 2 S content and said liquid hydrocarbon phase HCN with a low dissolved H 2 S content being treated in step d), or • a step d') in which the dissolved H 2 S of the intermediate gasoline cut MCN obtained from step d) is separated in order to produce an intermediate gasoline cut MCN with a low dissolved H 2 S content. a) fractionating the gasoline in order to recover a light gasoline cut LCN and a first heavy gasoline cut HCN; b) carrying out a first step for desulphurization of the first heavy gasoline cut HCN in the presence of a hydrodesulphurization catalyst and hydrogen, at a temperature in the range 160°C to 450°C, at a pressure in the range 0.5 to 8 MPa, with a liquid velocity in the range 0.5 to 20 h -1 and with a ratio between the flow rate of hydrogen, expressed in normal m 3 per hour, and the flow rate of feed to be treated, expressed in m 3 per hour under standard conditions, in the range 50 Nm 3 /m 3 to 1000 Nm 3 /m 3 in a manner such as to produce a first desulphurization effluent; c) partially condensing the first desulphurization effluent obtained from step b) in a manner such as to produce a gaseous phase essentially constituted by hydrogen and H 2 S and a liquid hydrocarbon phase HCN comprising dissolved H 2 S; d) separating the liquid hydrocarbon phase HCN into an intermediate gasoline cut MCN and a second heavy gasoline cut HHCN; e) carrying out a second step for desulphurization of the second heavy gasoline cut HHCN in the presence of a hydrodesulphurization catalyst and hydrogen, at a temperature in the range 160°C to 450°C, at a pressure in the range 0.5 to 8 MPa, with a liquid velocity in the range 0.5 to 20 h -1 and with a ratio between the flow rate of hydrogen, expressed in normal m 3 per hour, and the flow rate of feed to be treated, expressed in m 3 per hour under standard conditions, in the range 50 Nm 3 /m 3 to 1000 Nm 3 /m 3 in a manner such as to produce a desulphurized second heavy gasoline cut HHCN, • a step c') in which the dissolved H 2 S of the liquid hydrocarbon phase HCN obtained from step c) is separated in order to produce a liquid hydrocarbon phase HCN with a low dissolved H 2 S content and said liquid hydrocarbon phase HCN with a low dissolved H 2 S content being treated in step d), or • a step d') in which the dissolved H 2 S of the intermediate gasoline cut MCN obtained from step d) is separated in order to produce an intermediate gasoline cut MCN with a low dissolved H 2 S content.