A process for the selective hydrogenation in the gas phase of acetylene compounds containing 2 or 3 carbon atoms to the corresponding ethylene compounds is described. The process uses a catalyst in the form of spherules or extrudates containing palladium, at least one group IB metal, optionally at least one alkaline or alkaline-earth metal and alumina, in which at least 80% of the palladium and at least 80% of the group IB element are present in a volume at the periphery of the catalyst defined between a spherical or cylindrical surface of radius r.sub.1 corresponding to the average spherule or extrudate diameter and a spherical or cylindrical surface of radius r.sub.2 at least equal to 0.8r.sub.1. More particularly, the catalyst comprises an alumina, palladium in a proportion of 0.01% to 0.5% by weight, and group IB metal in a proportion of 0.001 to 0.02% by weight, with a weight ratio of group IB metal/palladium of 0.05 to 0.25.