Process for hydrogenating aromatic compounds containing sulfur impurities by contacting the same, at a temperature in the range of from 200* to 450*C and under a pressure of from 10 to 200 Kg/cm2, in a first step, with a catalyst containing a desulfurizing element selected from the oxides and/or sulfides of molybdenum, tungsten, nickel and cobalt, and an iron oxide, deposited on an alumina carrier used in an amount of 0.25 to 4 times the iron oxide amount, and in a second step, with a metal hydrogenation catalyst.