The role of zeolite in transformations of hydrocarbons produced from CO and H-2 over a Fischer-Tropsch cobalt catalyst under the conditions of multibed arrangement of the cobalt catalyst and the zeolite has been determined. Hydrocarbon conversion over the HBeta zeolite occurs via the bimolecular mechanism, as evidenced by a low methane yield and a high yield of unsaturated gaseous and liquid hydrocarbons. The conversion over the CaA zeolite obeys the unimolecular mechanism, as evidenced by the formation of increased amounts of methane and saturated gaseous C-2-C-4 hydrocarbons.