A process for preparing acrolein or acrylic acid or a mixture thereof as the target product from propane, in which propane is partially dehydrogenated under heterogeneous catalysis in a reaction zone A, molecular hydrogen formed is at least partly combusted to water, any water present in the product gas A formed in reaction zone A is removed therefrom and product gas A is otherwise used to charge a reaction zone B in which propylene formed in reaction zone A is partially oxidized in the presence of remaining propane to give the target product. The target product is removed from the product gas B formed in reaction zone B and propane present in the remaining residual gas is absorbed therefrom into a solvent and, after release from the absorbate, recycled into reaction zone A.