Abstract: A process for the preparation of polyolefins, polydienes and copolymers thereof by polymerization in solvents, liquid monomers or in the gaseous phase at a temperature between -20.degree. C. and 150.degree. C. using magnesium hydride, a halogen-containing transition metal compound of Group IV and an aluminium alkyl compound, characterized in that the polymerization is carried out in the presence of a catalyst system consists of(a) a magnesium compound having the general formulaMgH.sub.xwherein x is a number between 1 and 2, and more specifically 2; (b) a compound of a transition metal of Group IV having the general formulaMeHal.sub.4wherein Me is a transition metal, more specifically titanium, and Hal is a halogen, more specifically chlorine; and (c) an aluminium alkyl compound having the general formulaAlR.sub.n Hal.sub.(3-n)wherein R is a C.sub.1 -C.sub.6 alkyl residue, more specifically ethyl, Hal is a halogen, more specifically chlorine, and n is a number of from 1 to 3, and preferably 3.