Process for the selective hydrogenation of the acetylenic hydrocarbons of a C.sub.4 hydrocarbons cut, containing butadiene and at least 1% by weight of acetylenic hydrocarbons, without substantial hydrogenation of butadiene, wherein said hydrocarbons cut in liquid phase and hydrogen are contacted with a supported catalyst containing 0.05 to 0.5% by weight of palladium and 0.05 to 1% by weight of silver, the Ag/Pd ratio by weight being at least 0.7.