The invention describes a process for producing sulfuric acid by catalytic oxidation of SO2 to SO3 and subsequent absorption of the SO3 in sulfuric acid, wherein the SO3 is introduced into a first absorption stage (primary absorber) and at least partly absorbed there in concentrated sulfuric acid, wherein the SO3 not absorbed in the first absorption stage is supplied to a second absorption stage (secondary absorber) for the further absorption in concentrated sulfuric acid, and wherein the sulfuric acid is cooled after passing through the two absorption stages. The cooling of the sulfuric acid is effected in at least two heat exchangers connected in parallel, wherein one of the at least two heat exchangers is operated as partial evaporator and is cooled with boiler feed water/steam and the other one is cooled with cooling water and operated as pure acid cooler.