A process for total hydrogenation of polyunsaturated compounds that have n nonsaturations that are contained in a hydrocarbon feedstock in the presence of a catalytic reactor with a hydrogen-selective membrane is described. This process comprises the introduction of said feedstock that is co-mixed with hydrogen into a reaction zone of said reactor, the contact of hydrogen with the face that is upstream from said membrane, which is inorganic and porous, then the catalytic reaction of said feedstock with hydrogen that has selectively traversed the membrane.