Catalyst for the selective hydrogenation of multi-unsaturated organic compounds, in particular of diolefins and dienes in mixtures with other hydrocarbons; the catalyst is characterized by(A) a metal component from one or more elements of Group VIII of the Periodic Table on(B) a support material on the basis(b.sub.1) of one or more n-semiconducting oxides of one or more elements from the Subgroups IVb, Vb and VIb of the Periodic Table or of thorium or cerium, or respectively on the basis(b.sub.2) of one or more n-semiconducting mixed oxide systems of the formula Me.sub.2 Me.sub.1 (0).sub.x, where Me.sub.1 is an element of the group defined in (b.sub.1), Me.sub.2 an alkaline earth metal or an element different from Me.sub.1 or the group defined in (b.sub.1), and x signifies the number of oxygen atoms required for the saturation of Me.sub.1 and Me.sub.2 to the range of an n-semiconducting state;the hydrogen chemisorption capacity, expressed as the atomic ratio between chemisorbed hydrogen atoms and metal atoms of the metal component (A) present on the surface of the metal particles, (H/Me.sub.A), being at least 0.6:1.