A process for the combined hydrodesulfurization and hydroconversion of certain heavy hydrocarbon feedstocks is disclosed. Specifically, asphaltene-containing feedstocks, such as residua feedstocks, are initially contacted with a hydrodesulfurization catalyst which selectively avoids the conversion of the asphaltene agglomerates and metal-containing compounds therein, so that said feedstock is at least partially desulfurized, and then is contacted with an alkali metal in a conversion zone at elevated temperatures and in the presence of added hydrogen so that said feedstock is both further desulfurized and hydroconverted, preferably so that at least about 50 percent of the 1050.degree.F+ portion of the feedstock is converted to lower boiling products. In this manner the catalyst is maintained for long periods, while at the same time advantage is taken of the ability of the alkali metal desulfurization agent to both desulfurize and upgrade the hydrocarbon feedstock by the hydroconversion of the higher boiling components thereof.