Abstract: Process for upgrading a sulfur-containing feedstock comprising a hydrocarbon mixture substantially boiling in the gasoline range which process comprises the following steps:1) contacting the feedstock of a temparature of about 300.degree. C. to about 600.degree. C., a pressure of about 1 bar to about 40 bar and a space velocity of about 0.5 to about 10 g/g/h, with a catalyst which comprises a crystalline (metallo)silicate having an X-ray diffraction pattern containing the four strongest lines at interplanar spacings (d) expressed in .ANG., of 11.1.+-.0.2, 10.0.+-.0.2, 3.84.+-.0.07 and 3.72.+-.0.06, and2) contacting at least a fraction of the product obtained in step 1) at a temperature of about 200.degree. C. to about 600.degree. C., a pressure of about 20 bar to about 100 bar and a space velocity of about 0.