Process for the preparation of a mixture comprising C.sub.5+ linear olefins, which process comprises the steps of (a) reacting carbon monoxide and hydrogen in the presence of an effective amount of Fischer-Tropsch catalyst under Fischer-Tropsch reaction conditions; (b) separating from the hydrocarbon mixture thus prepared at least one hydrocarbon fraction, of which at least 95% by weight consists of hydrocarbons containing 15 carbon atoms or more; (c) contacting this hydrocarbon fraction with hydrogen in the presence of an effective amount of hydrogenation catalyst under hydrogenation conditions; (d) subjecting the hydrogenated hydrocarbon fraction thus obtained to a mild thermal cracking treatment; and (e) separating from the cracked product thus prepared the mixture comprising C.sub.5+ linear olefins.