.alpha.,.beta.-ethylenically unsaturated aldehydes and/or carboxylic acids are prepared by means of a two-stage catalytic gas-phase oxidation in which a gas mixture comprising at least an alkane or alkene having from three to six carbon atoms and oxygen is subjected to a catalytic oxidation reaction, in the first stage (1). oxygen is added to the gases produced in the first stage (1) and the resulting mixture is introduced into the second stage (2) in which it is subjected to a further catalytic oxidation reaction. In the process of the present invention, a signal which correlates with the oxygen content of the reaction gases before and/or after the addition of oxygen between the first and second stages (1, 2) is generated and the oxygen addition is regulated as a function of the signal. Also provided are an apparatus for regulating a process for preparing .alpha.,.beta.-ethylenically unsaturated aldehydes and/or carboxylic acids and an apparatus for preparing these substances using the regulating apparatus of the present invention.