Process for reducing the content of compounds of the sulphide type of formula R1-S-R2, with R1 and R2 selected from the methyl (CH 3) and ethyl (C 2 H 5) radicals, in a gasoline containing diolefins, mono-olefins and sulphur, in which: A) the gasoline in a mixture with a light gasoline cut recycled from step C) and hydrogen are brought into contact in a reactor with catalyst A comprising at least one metal of group Vlb and at least one non noble metal of group VIII deposited on a support, step A) being carried out at a temperature in the reactor comprised between 60°C and 150°C with a liquid hourly space velocity (LHSV) comprised between 1 h -1 and 10 h -1, a pressure comprised between 0.5 and 5 MPa and with a ratio by volume (added H 2 /mixture of gasolines) comprised between 1 to 40 normal litres of hydrogen per litre of the mixture of gasolines (vol/vol), so as to produce an effluent having a content of diolefins and a content of compounds of the sulphide type of formula R1-S-R2, with R1 and R2 selected from the methyl (CH 3) and ethyl (C 2 H 5) radicals lower than that that of the starting gasoline; B) said effluent originating from step A) is sent into a fractionating column in order to separate at the top of the column a light gasoline cut containing hydrocarbons having less than 6 carbon atoms per molecule and at the bottom of the column a heavy gasoline cut containing hydrocarbons having 6 and more than 6 carbon atoms per molecule; C) a part of the light gasoline cut originating from step B) is recycled into the reactor of step A) with a recycle ratio comprised between 0.1 and 0.7, in which catalyst A comprises: • a content of oxide of the metal of group Vlb comprised between 4 and 20% by weight with respect to the total weight of the catalyst, • a content of oxide of the metal of group VIII comprised between 4 and 15% by weight with respect to the total weight of the catalyst, • a degree of sulphurization of the metals constituting said catalyst at least equal to 60%, • a molar ratio between the non noble metal of group VIII and the metal of group Vlb comprised between 0.6 and 8 mol/mol, • a specific surface area of the catalyst comprised between 30 and 300 m 2 /g. A) the gasoline in a mixture with a light gasoline cut recycled from step C) and hydrogen are brought into contact in a reactor with catalyst A comprising at least one metal of group Vlb and at least one non noble metal of group VIII deposited on a support, step A) being carried out at a temperature in the reactor comprised between 60°C and 150°C with a liquid hourly space velocity (LHSV) comprised between 1 h -1 and 10 h -1, a pressure comprised between 0.5 and 5 MPa and with a ratio by volume (added H 2 /mixture of gasolines) comprised between 1 to 40 normal litres of hydrogen per litre of the mixture of gasolines (vol/vol), so as to produce an effluent having a content of diolefins and a content of compounds of the sulphide type of formula R1-S-R2, with R1 and R2 selected from the methyl (CH 3) and ethyl (C 2 H 5) radicals lower than that that of the starting gasoline; B) said effluent originating from step A) is sent into a fractionating column in order to separate at the top of the column a light gasoline cut containing hydrocarbons having less than 6 carbon atoms per molecule and at the bottom of the column a heavy gasoline cut containing hydrocarbons having 6 and more than 6 carbon atoms per molecule; C) a part of the light gasoline cut originating from step B) is recycled into the reactor of step A) with a recycle ratio comprised between 0.1 and 0.7, • a content of oxide of the metal of group Vlb comprised between 4 and 20% by weight with respect to the total weight of the catalyst, • a content of oxide of the metal of group VIII comprised between 4 and 15% by weight with respect to the total weight of the catalyst, • a degree of sulphurization of the metals constituting said catalyst at least equal to 60%, • a molar ratio between the non noble metal of group VIII and the metal of group Vlb comprised between 0.6 and 8 mol/mol, • a specific surface area of the catalyst comprised between 30 and 300 m 2 /g.