A gas mixture containing molecular oxygen and 15 to 60 vol. % SO2 flows through a first catalyst layer containing a catalyst containing vanadium pentoxide and immediately afterwards, through a second catalyst layer containing a catalyst containing iron. Said gas mixture is guided into the first catalyst layer at an entry temperature of 350 to 600 °C, said first catalyst layer containing a granular V205 catalyst and 20 to 80 wt. % catalytically inactive inert material. Immediately afterwards, the gas mixture is guided into the second catalyst layer at a temperature of 500 to 750 °C. The catalyst in the second catalyst layer preferably contains 3 to 30 wt. % arsenic oxide. The result is preferably a product gas containing SO3 with a SO2:SO3 volume ratio of at most 0.1.