A process for preparing maleic anhydride by heterogeneously catalyzed gas-phase oxidation of an n-butene-containing hydrocarbon stream by means of oxygen-containing gases in a shell-and-tube reactor having two successive reaction zones, where the first, feed-side reaction zone contains at least one catalyst which is suitable for the oxydehydrogenation of n-butenes to 1,3-butadiene and the second, product-side reaction zone contains at least one catalyst which is suitable for the oxidation of 1,3-butadiene to maleic anhydride, is carried out using a shell-and-tube reactor which has at least one heat transfer medium circuit in the region of the first, feed-side reaction zone and at least one further heat transfer medium circuit in the region of the second, product-side reaction zone.