In a process for the production of olefins in two stages wherein, in the first stage, heavy petroleum fractions are hydrogenated in the presence of hydrogen and a hydrogenation catalyst and, in the second stage, the thus-hydrogenated fractions are subjected to thermal cracking in the presence of steam, the improvement which comprises employing as the hydrogenation catalyst a support-free catalyst consisting essentially of elements from Groups VIb, VIIB, and VIII of the periodic table of the elements in the form of the metals, metal oxides, metal sulfides, or organometal complexes, or mixtures thereof.