This invention relates to a process for treatment of a gasoline comprising diolefins, olefins, and sulfur-containing compounds including mercaptans, in which: Gasoline is injected into a distillation column comprising at least one reaction zone to produce a desulfurized light gasoline; with the process also comprising the following stages: An intermediate gasoline fraction is drawn off at a level located above the reaction zone; A heavy gasoline comprising the majority of the sulfur-containing compounds is drawn off at the bottom of the column; In a demercaptization reactor, said intermediate gasoline fraction is brought into contact with a second catalyst to produce an effluent that contains sulfides; The effluent that is obtained from the demercaptization reactor is recycled in the distillation column (3).