A process for preparing acrolein or acrylic acid or a mixture thereof from propane, by A) feeding to a first reaction zone A at least two gaseous, propane-comprising feed streams, at least one of which comprises fresh propane, and, in reaction zone A, subjecting their propane fed in this way to a heterogeneously catalyzed dehydrogenation to obtain a product gas mixture A comprising propane and propylene, B) conducting product gas mixture A out of reaction zone A and, in a first separation zone A, removing at least a portion of the constituents, other than propane and propylene, present in product gas mixture A, and using remaining product gas mixture A' comprising propane and propylene C) in a second reaction zone B to charge at least one oxidation reactor and, in the at least one oxidation reactor, subjecting the propylene present in product gas mixture A' to a heterogeneously catalyzed gas phase partial oxidation with molecular oxygen to give a product gas mixture B comprising acrolein or acrylic acid or a mixture thereof as the target product and also excess molecular oxygen, D) conducting product gas mixture B out of reaction zone B and, in a second separation zone B, removing target product present in product gas mixture B, and, of the remaining residual gas comprising unconverted propane, molecular oxygen and possibly unconverted propylene, recycling at least a portion comprising unconverted propane, molecular oxygen and possibly unconverted propylene as one of the at least two propane-comprising feed streams into reaction zone A, wherein this recycling into reaction zone A along the reaction path of the heterogeneously catalyzed dehydrogenation of propane in reaction zone A is effected such that, at the feed point, at least 5 mol% of the propane fed to reaction zone A via the other feed streams has already been converted under dehydrogenating conditions in reaction zone A. A) feeding to a first reaction zone A at least two gaseous, propane-comprising feed streams, at least one of which comprises fresh propane, and, in reaction zone A, subjecting their propane fed in this way to a heterogeneously catalyzed dehydrogenation to obtain a product gas mixture A comprising propane and propylene, B) conducting product gas mixture A out of reaction zone A and, in a first separation zone A, removing at least a portion of the constituents, other than propane and propylene, present in product gas mixture A, and using remaining product gas mixture A' comprising propane and propylene C) in a second reaction zone B to charge at least one oxidation reactor and, in the at least one oxidation reactor, subjecting the propylene present in product gas mixture A' to a heterogeneously catalyzed gas phase partial oxidation with molecular oxygen to give a product gas mixture B comprising acrolein or acrylic acid or a mixture thereof as the target product and also excess molecular oxygen, D) conducting product gas mixture B out of reaction zone B and, in a second separation zone B, removing target product present in product gas mixture B, and, of the remaining residual gas comprising unconverted propane, molecular oxygen and possibly unconverted propylene, recycling at least a portion comprising unconverted propane, molecular oxygen and possibly unconverted propylene as one of the at least two propane-comprising feed streams into reaction zone A, wherein this recycling into reaction zone A along the reaction path of the heterogeneously catalyzed dehydrogenation of propane in reaction zone A is effected such that, at the feed point, at least 5 mol% of the propane fed to reaction zone A via the other feed streams has already been converted under dehydrogenating conditions in reaction zone A.