We study the polymerisation of a series of unstrained cyclic and acyclic dienes with the catalytic system of Mo(CO)(5)PPh3/alkylaluminum. The Mo(CO)(5)PPh3/alkylaluminum catalyse the nonmetathesis polymerisation, through a pair of ionic complexes similar to that of Ziegler-Natta mechanism, and not through the ROMP (Ring-Opening-Metathesis-Polymerisation) mechanism followed by strained olefins. Because of the nature of these complexes the reactivity is lower with respect to that of a common Ziegler-Natta catalyst, such as Cp2TiCl2/Et3Al2Cl3, as it is demonstrated, by means of kinetics and ESR measurements, in the case of the polymerisation of of 1,5-cyclooctadiene. Similarly to the Ziegler-Natta catalysts, they give cyclised products in the polymerisation of 1,5-hexadiene and 1,7-octadiene, and the 1,4-cis unit in the case of the polypentadienes. Finally we find that they are active catalysts for the polymerisation of styrene.