A combination process for the desulfurization of asphaltenecontaining black oils. The charge stock in admixture with hydrogen and a recycle stream containing a high percentage of asphaltenes is subjected to a first-stage catalytic desulfurization zone. The effluent from the first stage is deasphalted to produce a deasphalted oil stream and a residuum stream. The deasphalted oil stream in admixture with hydrogen is subjected to a second-stage catalytic desulfurization zone and at least a portion of the residuum stream is recycled to the first stage catalytic desulfurization zone.