The present invention relates to a process for the continuous catalytic complete or partial oxidation of a starting gas containing from 0.1 to 66% by volume of sulphur dioxide plus oxygen, in which the catalyst is kept active by means of pseudoisothermal process conditions with introduction or removal of energy. In addition, the present invention relates to an apparatus for the continuous catalytic complete or partial oxidation of a starting gas containing sulphur dioxide and oxygen, characterized by at least one tube contact apparatus which is an upright heat exchanger composed of at least one double-walled tube whose catalyst-filled inner tube forms a reaction tube, with heat being transferred in cocurrent around the reaction tube and an absorber for separating off SO3 being installed downstream of the tube contact apparatus. The reactivity of the catalyst is preset by mixing with inert material. The apparatus of the invention is particularly suitable for carrying out the process of the invention.