The present invention concerns a heterogeneous catalyst particularly suited to the metathetic reactions of olefins in liquid or gas phase. Such a catalyst generally includes catalytically active species of tungsten on an inorganic support. The catalyst in accordance with the invention is prepared by vaporizing a precursor of tungsten, such as tungsten oxychloride or hexachloride and then routing the vapor of the tungsten-containing reagent into a reaction space, where the vapor is brought to interaction with the support material at approximately 160.degree. to 500.degree. C. The vapor pressure of the tungsten-containing reagent is kept sufficiently high, and the duration of interaction with the support sufficiently long, to keep the amount of the reagent at least equal to the number of available bonding sites of the support, whereby the bonding of the tungsten-containing reagent to the support surface is determined by the surface properties of the support. The catalyst can be posttreated after its preparation to modify its catalytic activity. The specific activity of the catalytic metal species of the catalyst according to the invention is high.