A process for jointly carrying out selective hydrogenation of polyunsaturated compounds into monounsaturated compounds contained in gasolines, and for transforming light sulphur-containing compounds into heavier compounds by reaction with unsaturated compounds, said process employing a supported catalyst comprising at least one metal from group VIB and at least one non-noble metal from group VIII used in the sulphurized form, deposited on a specific support comprising a metal aluminate of the MAl.sub.2O.sub.4 type with a metal M selected from the group constituted by nickel and cobalt, and comprising bringing the feed into contact with the catalyst at a temperature in the range of 80.degree. C. to 220.degree. C. at a liquid hourly space velocity in the range of 1 h.sup.-1 to 10 h.sup.-1 and at a pressure in the range of 0.5 to 5 MPa.