A multiple stage process is described for the catalytic hydrodesulfurization and hydrodemetallization of a residual petroleum oil boiling above the gasoline range. The product of the process comprises essentially material boiling above the gasoline range and comprises little material boiling below the initial boiling point of the residual oil feed. The hydrodesulfurization-demetallization process comprises an initial stage involving relatively high hydrogen pressure in the presence of a catalyst comprising a relatively low proportion of catalytically active hydrogenation metals. Hydrogen sulfide is removed from the process after the initial stage and the process employs a final stage in series having a relatively lower hydrogen pressure and a catalyst comprising a relatively higher proportion of hydrogenation metals. The stream entering the final stage contains hydrogen sulfide or a hydrogen sulfide precursor added thereto and contains an amount up to 10, 20 or even 25 weight percent of the asphaltene content of the charge to the first stage while the effluent from the final stage is essentially free of asphaltenes.