A process for the catalytic dehydrogenation of a first unsaturated hydrocarbon to form a second unsaturated hydrocarbon which has one olefinically unsaturated bond more than the first unsaturated hydrocarbon and otherwise an unchanged carbon skeleton, which process comprises contacting in a first step a feed comprising the first unsaturated hydrocarbon with a first dehydrogenation catalyst having a temperature parameter T.sub.1 and a selectivity parameter S.sub.1, and contacting in a second step a reaction product of the first step comprising the first unsaturated hydrocarbon and the second unsaturated hydrocarbon with a second dehydrogenation catalyst having a temperature parameter T.sub.2 and a selectivity parameter S.sub.2, such that T.sub.1