Methods for the combined elimination of both ammonia and lower alkanes and/or hydrogen, which are contained in one or more waste gas streams in an industrial plant, are disclosed herein. The method is effectuated by combined oxidation and reduction according to the reduction-oxidation process, wherein the ammonia and the lower alkanes and/or hydrogen are completely or partially reacted by chemical reaction to form nitrogen, carbon dioxide and water. The waste gas stream containing ammonia and lower alkanes and/or hydrogen is passed over one or more catalysts for the combined oxidation and reduction, and the oxygen content in the waste gas stream is set in such a way that ammonia and the lower alkanes and/or hydrogen are oxidized first in an oxidation zone to form nitrogen, carbon dioxide and water, and the nitrogen oxides resulting therefrom are subsequently reduced in a reduction zone to form elemental nitrogen.