A reactor in the form of a cylinder or prism for carrying out an autothermal gas-phase dehydrogenation of a hydrocarbon-comprising gas stream by means of an oxygen-comprising gas stream to give a reaction gas mixture over a heterogeneous catalyst configured as monolith, where - the interior of the reactor is divided by a cylindrical or prismatic gastight housing G which is arranged in the longitudinal direction of the reactor into - an inner region A having one or more catalytically active zones, in which a packing composed of monoliths stacked on top of one another, next to one another and behind one another and before each catalytically active zone in each case a mixing zone having solid internals are provided, and - an outer region B arranged coaxially to the inner region A, and - a heat exchanger is provided at one end of the reactor subsequent to the housing G, - with one or more feed lines for the hydrocarbon-comprising gas stream to be dehydrogenated, - with one or more feed lines which can be regulated independently of one another, where each feed line supplies one or more distribution chambers, for the oxygen-comprising gas stream into each of the mixing zones and - with a discharge line for the reaction gas mixture of the autothermal gas-phase dehydrogenation, where - the outer region B can be supplied with a gas which is inert under the reaction conditions of the autothermal gas-phase dehydrogenation and - the hydrocarbon-comprising gas stream to be dehydrogenated is introduced via a feed line into the heat exchanger, is heated in the heat exchanger by means of the reaction gas mixture in countercurrent by indirect heat exchange and conveyed further to the end of the reactor opposite the heat exchanger, redirected there, introduced via a flow equalizer into the inner region A and mixed with the oxygen-comprising gas stream in the mixing zones, whereupon the autothermal gas-phase dehydrogenation takes place in the inner region A of the reactor, wherein the inner region A is insulated from the outer region B of the reactor by means of a microporous high-performance insulation material having a thermal conductivity λ at temperatures up to 700°C of less than 0.05 W/m*K. - the interior of the reactor is divided by a cylindrical or prismatic gastight housing G which is arranged in the longitudinal direction of the reactor into - an inner region A having one or more catalytically active zones, in which a packing composed of monoliths stacked on top of one another, next to one another and behind one another and before each catalytically active zone in each case a mixing zone having solid internals are provided, and - an outer region B arranged coaxially to the inner region A, and - a heat exchanger is provided at one end of the reactor subsequent to the housing G, - with one or more feed lines for the hydrocarbon-comprising gas stream to be dehydrogenated, - with one or more feed lines which can be regulated independently of one another, where each feed line supplies one or more distribution chambers, for the oxygen-comprising gas stream into each of the mixing zones and - with a discharge line for the reaction gas mixture of the autothermal gas-phase dehydrogenation, where - the outer region B can be supplied with a gas which is inert under the reaction conditions of the autothermal gas-phase dehydrogenation and - the hydrocarbon-comprising gas stream to be dehydrogenated is introduced via a feed line into the heat exchanger, is heated in the heat exchanger by means of the reaction gas mixture in countercurrent by indirect heat exchange and conveyed further to the end of the reactor opposite the heat exchanger, redirected there, introduced via a flow equalizer into the inner region A and mixed with the oxygen-comprising gas stream in the mixing zones, whereupon the autothermal gas-phase dehydrogenation takes place in the inner region A of the reactor,