In a process for the preparation of acrolein or acrylic acid or a mixture thereof from propane, the propane is subjected, in a first reaction stage, to a partial dehydrogenation under heterogeneous catalysis to give propene, of the components contained in the product gas mixture formed in the first reaction stage other than propene and propane at least a portion of the molecular hydrogen present is then separated off from said mixture and the product gas mixture is then used for the preparation of acrolein and/or acrylic acid by gas-phase catalytic propylene oxidation, molecular nitrogen being present for diluting the reaction gas mixture during the propylene oxidation.