Disclosed is a two-stage catalytic process for hydrodemetallation and hydrodesulfurization of heavy hydrocarbon streams containing asphaltenes and a substantial amount of metals. The first stage of this process comprises contacting the feedstock in a first reaction zone with hydrogen and a demetallation catalyst comprising hydrogenation metal selected from Group VIB and/or Group VIII deposed on a large-pore, high surface area inorganic oxide support; the second stage of the process comprises contacting the effluent from the first reaction zone with a catalyst consisting essentially of hydrogenation metal selected from Group VIB deposed on a smaller-pore, catalytically active support comprising alumina, said second-stage catalyst having a surface area within the range of about 150 m.sup.2 /gm to about 300 m.sup.2 /gm, having a majority of its pore volume in pore diameters within the range of about 80 A to about 130 A, and the catalyst has a pore volume within the range of about 0.4 cc/gm to about 0.9 cc/gm.