Dry polymerization of olefins in reaction vessels arranged in series

A method of producing polymers having a molecular weight generally higher than 50,000, by the dry polymerization of olefins of the formula CH.sub.2 .dbd. CHR, in which R is selected from the group consisting of a hydrogen atom and an alkyl radical having from 1 to 8 carbon atoms, in reaction vessels in which the solid polymer in course of formation is kept in the fluidized state by an upward stream of a gaseous mixture containing the olefin or olefins to be polymerized, the reaction vessels being arranged in a series in which the solid polymer in course of formation flows successively from the first reaction vessel through to the last reaction vessel from which the polymer is discharged while a separate recycle is maintained for each reaction vessel with respect to the gaseous mixture of olefin or olefins whereby the said gaseous mixture issuing from one reaction vessel is recycled for reintroduction into the same reaction vessel, polymerization being initiated by introducing into the first reaction vessel a catalyst comprising a solid compound of a transition metal from the subgroups IVa, Va and VIa of the periodic table, and at least one cocatalyst comprising an organo-metallic compound of a metal from group II or III of the periodic table, introducing cocatalyst into the first reaction vessel in an amount such that the atomic ratio of the metal of the co-catalyst or cocatalysts to the transition metal of the catalyst is between 0.1 to 10, and introducing an additional quantity of at least one cocatalyst into at least one of the reaction vessels other than the first.