A process for heterogeneously catalyzed partial dehydrogenation of a hydrocarbon, in which a reaction gas mixture input stream comprising the hydrocarbon to be dehydrogenated is conducted through a fixed catalyst bed disposed in a shaft and the reaction gas mixture input stream is obtained in the shaft by metering an input gas II comprising molecular oxygen upstream of the fixed catalyst bed into an input gas stream I which comprises molecular hydrogen and the hydrocarbon to be dehydrogenated and is flowing within the shaft toward the fixed catalyst bed.