Abstract: In the continuous production of oleum having a concentration of 10 to 45% by weight SO.sub.3 and/or sulfuric acid having a concentration of 94 to 100% by weight H.sub.2 SO.sub.4 by burning sulfur with atomospheric oxygen on the principle of overstoichiometric or understoichiometric burning, cooling the resulting SO.sub.2 -containing gas to 390.degree.-480.degree. C., catalytically reacting the cooled gas to SO.sub.3 -containing gas on a vanadium-containing catalyst on the principle of single- or double-contact catalysis, absorbing the SO.sub.3 -containing gas after cooling and, optionally, separating liquid from the gas after absorption, followed by recovering energy, the improvement which comprises effecting the burning of the sulfur with atomospheric oxygen in the presence of a dry SO.sub.2 -containing gas which contains up to 5,000 ppm (NO).sub.x expressed as NO.