Abstract: Co dimerization is conducted of at least one monoolefin, for example a monoolefinic hydrocarbon such as ethylene, propylene or 1-butene, a halogenated monoolefin such as vinyl chloride, or an olefinic functional compound such as methyl acrylate, acrylonitrile, allyl acetate or vinyl acetate, with at least one polyolefin containing at least two conjugated or unconjugated ethylene bonds, for example a diene hydrocarbon such as 1,3-butadiene, piperylene, or isoprene or a polyolefin containing a carboxylic function, such as a fatty acid or a fatty acid ester having 14 to 24 carbon atoms in the fatty chain derived, for example, from a natural oil. The reaction is carried out in the presence of a catalytic system having general formula [RhX.sub.4 ][YR.sub.4 ] where X represents a halogen ion or a SO.sub.4.sup.--, SO.sub.3.sup.-, OH.sup.-, OR.sup.- or R.sup.