A process for preparing acrolein or acrylic acid or a mixture thereof from propane, in which A) - at least two gaseous propane-comprising feed streams, of which at least one comprises fresh propane, are fed to a first reaction zone A to form a reaction gas A; - in reaction zone A, reaction gas A is conducted through at least one catalyst bed in which partial heterogeneously catalyzed dehydrogenation of the propane forms molecular hydrogen and propylene; - molecular oxygen is fed to reaction zone A and, in reaction zone A, oxidizes at least a portion of molecular hydrogen present in reaction gas A to steam, and - product gas A which comprises propylene, propane and steam is withdrawn from reaction zone A; B) if appropriate, in a first separation zone I, steam present in product gas A is removed by condensation partly or fully by indirect and/or direct cooling of product gas A to leave a product gas A*; C) in a reaction zone B, product gas A or product gas A* is used, with feeding of molecular oxygen, to charge at least one oxidation reactor with a reaction gas B comprising propane, propylene and molecular oxygen, and the propylene present therein is subjected to a heterogeneously catalyzed partial gas phase oxidation to give acrolein or acrylic acid or a mixture thereof as the target product, and also product gas B comprising unconverted propane; D) product gas B is conducted out of reaction zone B and, in a second separation zone II, target product present therein is removed to leave a propane-comprising residual gas; E) if appropriate, a portion of residual gas having the composition of the residual gas is recycled as a propane-comprising feed stream into reaction zone A; F) in a separation zone III, propane present in residual gas which has not been recycled into reaction zone A and from which, if appropriate, any steam present therein has been removed beforehand partly or fully by condensation and/or any molecular hydrogen present therein has been removed beforehand partly or fully by means of a separating membrane is absorbed into an organic solvent by absorption from the residual gas to form a propane-comprising absorbate; and G) in a separation zone IV, the propane is removed from the absorbate and recycled into reaction zone A as a propane-comprising feed stream; which comprises oxidizing at least sufficient molecular hydrogen to steam in reaction zone A that the amount of hydrogen oxidized to steam in reaction zone A is at least 20 mol% of the amount of molecular hydrogen formed in reaction zone A. A) - at least two gaseous propane-comprising feed streams, of which at least one comprises fresh propane, are fed to a first reaction zone A to form a reaction gas A; - in reaction zone A, reaction gas A is conducted through at least one catalyst bed in which partial heterogeneously catalyzed dehydrogenation of the propane forms molecular hydrogen and propylene; - molecular oxygen is fed to reaction zone A and, in reaction zone A, oxidizes at least a portion of molecular hydrogen present in reaction gas A to steam, and - product gas A which comprises propylene, propane and steam is withdrawn from reaction zone A; - at least two gaseous propane-comprising feed streams, of which at least one comprises fresh propane, are fed to a first reaction zone A to form a reaction gas A; - in reaction zone A, reaction gas A is conducted through at least one catalyst bed in which partial heterogeneously catalyzed dehydrogenation of the propane forms molecular hydrogen and propylene; - molecular oxygen is fed to reaction zone A and, in reaction zone A, oxidizes at least a portion of molecular hydrogen present in reaction gas A to steam, and - product gas A which comprises propylene, propane and steam is withdrawn from reaction zone A; B) if appropriate, in a first separation zone I, steam present in product gas A is removed by condensation partly or fully by indirect and/or direct cooling of product gas A to leave a product gas A*; C) in a reaction zone B, product gas A or product gas A* is used, with feeding of molecular oxygen, to charge at least one oxidation reactor with a reaction gas B comprising propane, propylene and molecular oxygen, and the propylene present therein is subjected to a heterogeneously catalyzed partial gas phase oxidation to give acrolein or acrylic acid or a mixture thereof as the target product, and also product gas B comprising unconverted propane; D) product gas B is conducted out of reaction zone B and, in a second separation zone II, target product present therein is removed to leave a propane-comprising residual gas; E) if appropriate, a portion of residual gas having the composition of the residual gas is recycled as a propane-comprising feed stream into reaction zone A; F) in a separation zone III, propane present in residual gas which has not been recycled into reaction zone A and from which, if appropriate, any steam present therein has been removed beforehand partly or fully by condensation and/or any molecular hydrogen present therein has been removed beforehand partly or fully by means of a separating membrane is absorbed into an organic solvent by absorption from the residual gas to form a propane-comprising absorbate; and G) in a separation zone IV, the propane is removed from the absorbate and recycled into reaction zone A as a propane-comprising feed stream;