A method comprising subjecting fuel to combustion while the combustion atmosphere of the fuel is oscillated periodically and alternately between rich and lean conditions, leading the exhaust gas formed to a catalytic reactor, and bringing the exhaust gas into contact with a catalyst in the catalytic reactor to conduct catalytic reduction of nitrogen oxides contained in the exhaust gas, wherein the catalyst comprises as catalyst components: (A) an oxide catalyst component A comprising (a) ceria or (b) praseodymium oxide or (c) a mixture of oxides and/or a composite oxide of at least two elements selected from cerium, zirconium, praseodymium, neodymium, terbium, samarium, gadolinium and lanthanum; and (B) (d) a noble metal catalyst component B selected from platinum, rhodium, palladium and oxides thereof; under an oxygen concentration adjusted to the range of 0.1-1.0% at the exit of the catalytic reactor under the rich conditions.