A process reducing sulfides R1-S-R2, with R1 and R2 methyl or ethyl, in a gasoline containing diolefins, mono-olefins and sulphur: A) contacting gasoline in mixture with a light gasoline cut recycled from C) and hydrogen in a reactor with catalyst A at least one VIb metal and at least one non noble group VIII metal on a support, producing effluent having diolefins and sulfides R1-S-R2, with R1 and R2 methyl or ethyl radicals lower than that that of the starting gasoline; B) the effluent from A) is sent into a fractionating column separating at the top a light gasoline cut containing hydrocarbons having less than 6 carbon atoms per molecule and at the bottom a heavy gasoline cut containing hydrocarbons having 6 and more than 6 carbon atoms per molecule; C) recycling a part of the light gasoline from B) to the reactor of A) with a recycle ratio 0.1 to 0.7.