A process for the dehydrogenation of a C2 or C3 alkyl aromatic compound to a corresponding vinyl aromatic compound in a tubular reactor incorporating a spiral flow path. Preferred embodiments of the invention provide processes for the production of styrene or divinylbenzene by the catalytic dehydrogenation of ethylbenzene or diethylbenzene, respectively. A feedstock containing a C2 or C3 alkyl aromatic and steam is supplied into the inlet of a tubular reactor containing a dehydrogenation catalyst and comprising a hydrogen permeable outer wall. The alkyl aromatic compound is dehydrogenated to a corresponding vinyl aromatic compound with the attendant production of hydrogen. The feedstock and products of the dehydrogenation reactor are flowed along a longitudinal spiral flow path providing for an outward radial flow of hydrogen to provide a pressure gradient through the hydrogen permeable outer wall of the reactor with the flow of hydrogen therethrough. Hydrogen is removed from the outer wall of the reactor. The resulting vinyl aromatic product is recovered from the tubular reactor.