A catalyst is disclosed made from a porous inorganic carrier material impregnated with a metal component selected from palladium, rhodium, mixtures of palladium and rhodium, and mixtures of palladium and a metal of the copper group, in which the carrier has a bimodal pore radius distribution with a first pore radius distribution maximum in the range of up to 400 .ANG., preferably 50 to 350 .ANG., and with a proportion of at least 20%, relative to the overall pore volume, of macropores having a radius of at least 2,000 .ANG., preferably 5,000 to 20,000 .ANG..