A process is disclosed for the preparation of a hydrocarbon mixture by contacting in a first stage a feed mixture of hydrogen and carbon monoxide with an H.sub.2 /CO molar ratio of less than 1.0 with a trifunctional catalyst combination containing (a) at least one metal component having catalytic activity for conversions of a H.sub.2 /CO mixture into acyclic hydrocarbons, and/or acyclic oxygen-containing hydrocarbons, (b) at least one metal component for the conversion of an H.sub.2 O/CO mixture into an H.sub.2 /CO mixture, and (c) a certain crystalline silicate containing at least one trivalent metal selected from aluminum, iron, gallium, rhodium, chromium and scandium, wherein the molar ratio of the trivalent metal oxide to silica is less than 0.1; adjusting the H.sub.2 /CO molar to at least 1.5 by adding H.sub.2 O, if necessary; followed by contacting in a second stage at least the C.sub.2 - fraction of the reaction product from the first stage with a bifunctional catalyst combination containing at least one metal component with catalytic activity for converting an H.sub.2 /CO mixture into acyclic hydrocarbons and also at least one metal component with catalytic activity for converting an H.sub.2 O/CO mixture into an H.sub.2 /CO.sub.2 mixture.