Method of selective hydrogenation using a catalyst with controlled porosity

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 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 support and having a controlled porosity, and comprising bringing the feed into contact with the catalyst at a temperature in the range of 80 DEG C to 220 DEG C at a liquid hourly space velocity in the range of 1 h-1 to 10 h-1 and at a pressure in the range of 0.5 to 5 MPa.