Process for preparing phthalic anhydride by gas-phase oxidation of xylene, naphthalene or mixtures thereof in a shell-and-tube reactor thermostatted by means of a heat transfer medium over three or more different fixed-bed catalysts arranged in zones, wherein the process is carried out so that the maximum temperature in the second catalyst zone in the flow direction is up to 50.degree. C. lower than the maximum temperature in the first catalyst zone and the maximum temperature in the third zone from the gas inlet is from 30 to 100.degree. C. lower than that in the first catalyst zone.The process of the present invention makes it possible to prepare phthalic anhydride in high yields under industrially relevant conditions.