A process for the continuous heterogeneously catalyzed gas-phase oxidation of propylene to acrolein, acrylic acid or a mixture thereof in an oxidation reactor whose feed gas mixture comprises, apart from propylene and molecular oxygen as oxidant, only at least one diluent gas which is essentially inert under the conditions of the heterogeneously catalyzed gas-phase oxidation, where, in continuous operation, at least a part of the essentially inert diluent gas constituents present in the product gas mixture is separated off therefrom and is reused as a constituent of the feed to the oxidation reactor, wherein the essentially inert diluent gas of the feed gas mixture in continuous operation comprises more than 85% by volume of at least one saturated hydrocarbon having from 1 to 5 carbon atoms.