In a process for the heterogeneously catalyzed dehydrogenation in one or more reaction zones of one or more dehydrogenatable C.sub.2-C.sub.30-hydrocarbons in a reaction gas mixture comprising them, with at least part of the heat of dehydrogenation required being generated directly in the reaction gas mixture in at least one reaction zone by combustion of hydrogen, the hydrocarbon or hydrocarbons and/or carbon in the presence of an oxygen-containing gas, the reaction gas mixture comprising the dehydrogenatable hydrocarbon or hydrocarbons is brought into contact with a Lewis-acid dehydrogenation catalyst which has essentially no Bronsted acidity.