The invention concerns a process for the hydrodesulphurization of gasoline cuts for the production of gasolines with a low sulphur and mercaptans content. Said process comprises at least two hydrodesulphurization steps, HDS1 and HDS2, operated in parallel on two distinct cuts of the gasoline constituting the feed. The flow rate of hydrogen in the hydrodesulphurization step HDS2 is such that the ratio between the flow rate of hydrogen and the flow rate of feed to be treated is less than 80% of the ratio of the flow rates used to desulphurize in the hydrodesulphurization step HDS1.