A process for the selective hydrogenation in the gas phase of acetylene compounds containing 2 or 3 carbon atoms to the corresponding ethylene compounds in the presence of a catalyst in the form of spherules or extradates containing an alumina support, 0.01-0.5% by weight palladium, 0.001 to 0.5% by weight of at least one group IB metal, preferably silver, and optionally at least one alkaline or alkaline-earth metal, the weight ratio of the group IB metal to palladium being 0.05:1 to 0.25:1, in which catalyst at least 80% of the palladium and at least 80% of the group IB element are present in a volume at a periphery of the catalyst defined between a spherical or cylindrical surface of radius r.sub.1 corresponding to the average spherule or extradate diameter and a spherical or cylindrical surface of radius r.sub.2 at least equal to 0.8r.sub.1.