The invention relates to a process for the desulfurization of gasolines comprising a stage for fractionation of said gasoline into a light fraction that comprises thiophenic compounds such as thiophene or methylthiophenes, and a heavy fraction that concentrates the heaviest aromatic sulfur-containing compounds. The heavy fraction is treated by hydrodesulfurization, while the light fraction is brought into contact with a solid adsorbent that makes it possible to eliminate at least partially said light thiophenic compounds, whereby said adsorbent solid is regenerated by a flow internal to the process.