A process for the deep desulfurization of a heavy pyrolysis gasoline feedstock containing a diolefin concentration of from 100 ppmw to less than 3 wt%, an organic sulfur concentration in the range of from 75 ppmw to 2,000 ppmw and an aromatic concentration in the range of from 30 wt % to 85 wt% of the total weight of said heavy pyrolysis gasoline feedstock, wherein said process comprises: heating said heavy pyrolysis gasoline feedstock to a temperature sufficient to provide a heated pyrolysis gasoline feedstock having a portion of from 10 wt% to 80 wt% that is in a gaseous phase and another portion of from 20 wt% to 90 wt% that is in a liquid phase; introducing said heated pyrolysis gasoline feedstock that is in said liquid phase and said gaseous phase into a reactor vessel at a liquid hourly space velocity (LHSV) of 0.1 hr -1 to 10 hr -1, or more than one reactor vessel in series flow arrangement, that contains a hydrogenation catalyst and is operated in a downflow mode, wherein the hydrogenation catalyst comprises nickel/molybdenum on a support comprising alumina, silica, silica alumina, titania, or zirconia, the amount of nickel being from 0.01 wt% to 10 wt%, and the amount of molybdenum being from 3 wt% to 30 wt%, with the wt% being calculated based on the total weight of the catalyst and assuming the metal is in the oxide form; contacting said heated pyrolysis gasoline feedstock in the presence of an added hydrogen treat gas comprising at least 70 volume percent of molecular hydrogen and having an H 2 S concentration of greater than 150 ppmv and at most 2000 ppmv with said hydrogenation catalyst at a temperature in the range of from 175 °C to 275 °C and at an operating pressure in the range of from 2859 KPa to 5617 KPa (400 psig to 800 psig), the temperature being effective to selectively hydrogenate a substantial portion of the diolefins contained in said heated pyrolysis gasoline feedstock to monoolefins and a substantial portion of the organic sulfur in said heated pyrolysis gasoline feedstock to H 2 S, but not at a temperature to significantly hydrogenate the aromatic compounds contained in said heated pyrolysis gasoline feedstock; yielding from said reactor vessel, or more than one reactor vessel in series flow arrangement, a reactor effluent; and separating H 2 S and unreacted hydrogen from said reactor effluent and recovering from said reactor effluent a low-sulfur pyrolysis gasoline product that contains less than 30 ppm organic sulfur compounds. heating said heavy pyrolysis gasoline feedstock to a temperature sufficient to provide a heated pyrolysis gasoline feedstock having a portion of from 10 wt% to 80 wt% that is in a gaseous phase and another portion of from 20 wt% to 90 wt% that is in a liquid phase; introducing said heated pyrolysis gasoline feedstock that is in said liquid phase and said gaseous phase into a reactor vessel at a liquid hourly space velocity (LHSV) of 0.1 hr -1 to 10 hr -1, or more than one reactor vessel in series flow arrangement, that contains a hydrogenation catalyst and is operated in a downflow mode, wherein the hydrogenation catalyst comprises nickel/molybdenum on a support comprising alumina, silica, silica alumina, titania, or zirconia, the amount of nickel being from 0.01 wt% to 10 wt%, and the amount of molybdenum being from 3 wt% to 30 wt%, with the wt% being calculated based on the total weight of the catalyst and assuming the metal is in the oxide form; contacting said heated pyrolysis gasoline feedstock in the presence of an added hydrogen treat gas comprising at least 70 volume percent of molecular hydrogen and having an H 2 S concentration of greater than 150 ppmv and at most 2000 ppmv with said hydrogenation catalyst at a temperature in the range of from 175 °C to 275 °C and at an operating pressure in the range of from 2859 KPa to 5617 KPa (400 psig to 800 psig), the temperature being effective to selectively hydrogenate a substantial portion of the diolefins contained in said heated pyrolysis gasoline feedstock to monoolefins and a substantial portion of the organic sulfur in said heated pyrolysis gasoline feedstock to H 2 S, but not at a temperature to significantly hydrogenate the aromatic compounds contained in said heated pyrolysis gasoline feedstock; yielding from said reactor vessel, or more than one reactor vessel in series flow arrangement, a reactor effluent; and separating H 2 S and unreacted hydrogen from said reactor effluent and recovering from said reactor effluent a low-sulfur pyrolysis gasoline product that contains less than 30 ppm organic sulfur compounds.