Abstract: NO.sub.x, where x is 1 and 2, in exhaust gases is reduced over heterogeneous catalysts with hydrocarbons, carbon monoxide, hydrogen or mixtures thereof in the presence of oxygen from 100 to 650.degree. C. and an absolute pressure of from 0.5 to 50 bar by a process in which the heterogeneous catalysts used are bimodal or polymodal compounds of the general formula IA.sub.1-x M.sub.2 O.sub.4 (I),which, if required, are doped with rare earth metals, noble metal, titanium, vanadium, molybdenum, tungsten or mixtures thereof, and whereA is magnesium, calcium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper, zinc, tin or mixtures thereof,M is aluminum, gallium, indium, tin, chromium, manganese, iron, cobalt, nickel, copper, zinc or mixtures thereof andx is from 0 to 0.