A process for selective hydrogenation of polyunsaturated compounds that are contained in a hydrocarbon feedstock in the presence of a catalytic reactor with a hydrogen-selective membrane comprises a) the introduction of said feedstock co-mixed with a first amount hydrogen into a reaction zone of said reactor, b) the contact of a second amount hydrogen with the upstream face of the membrane, which is inorganic and porous, then c) the catalytic reaction of the feedstock with hydrogen that has selectively traversed the membrane.