The invention relates to a process for the selective hydrogenation of alkynes and dienes in C2-C5.sup.+-olefin mixtures,--in C2- or C3-streams of the olefin preparation by cracking. The method comprises conducting the hydrogenation in the presence of a catalyst particle comprising (a) a metal of the tenth group of the Periodic Table, (b) a metal of the eleventh group of the Periodic Table and (c) optionally a compound of a metal of the first or second group of the Periodic Table. Components (a) and (b), and optionally (c), are applied to a support selected from the group consisting of silica, titanium dioxide, zirconium oxides, spinels, zinc aluminates, zinc titanate, aluminosilicates and mixtures thereof. The metal of the eleventh group is distributed homogeneously over the cross-section of the catalyst particle, and the metal of the tenth group is present in an edge layer close to the surface of the catalyst particle.