The invention relates to a process for direct oxidation into sulfur and/or into sulfate of sulfur-containing compounds that are contained in an amount that is less than 10% by volume in a gas, in which said gas is brought into contact with an oxidation catalyst that comprises a substrate and an active phase that comprises iron in a proportion of between 2 and 5% by weight of the oxidation catalyst at a temperature of less than 200° C. and in the presence of oxygen.