An α,β-unsaturated aldehyde and/or an α,β-unsaturated carboxylic acid are prepared by gas phase oxidation of alkene with molecular oxygen over a fixed catalyst bed comprising a bed of hollow cylindrical shaped catalyst bodies having a multimetal oxide active composition. The fixed catalyst bed comprises at least three successive reaction zones; the highest local temperature in the fixed catalyst bed does not occur in the reaction zone closest to the reactor outlet; the highest local temperature in the fixed catalyst bed does not occur in the reaction zone closest to the reactor inlet; and the value WT=(ED−ID)/2 in the reaction zone in which the highest local temperature in the fixed catalyst bed occurs is lower than in the other reaction zones, in which ED is the external diameter and ID is the internal diameter of the shaped catalyst body. The yield of the products of value is enhanced in this way.