Disclosed is a process for the catalytic dehydrogenation of alkanes so as to form the corresponding olefins. The reaction mixture is subjected to membrane separation of hydrogen, in a separate unit. Preferably a plurality of alternating reaction and separation units is used. The process of the invention serves the purpose of reducing coke formation on the catalyst, and also of achieving a higher alkane conversion without a similar increase in coke formation. The process can also be used for the production of hydrogen.