A method is described for the polymerization of isobutylene and, in particular, the copolymerization of isobutylene and isoprene to produce butyl rubber, by contacting the monomers with a catalyst prepared from: (a) an organoaluminum compound (e.g. Al(C.sub.2 H.sub.5).sub.2 Cl) and (b) a compound represented by the formula X'.sub.n M.sub.e Y.sub.m in which X' is a halogen atom; Y is oxygen, sulphur or a functional group selected from the alkoxies, esters, amides, simple or substituted alkyls, cycloalkyls, aromatics, arenes, phosphines, acetylacetones and oximes; Me is an element selected from Ti, Sn, Zn, B, Al, Hg, Pb, W, Sb, Ge, V, Zr, As, Bi and Mo; n and m are whole numbers whose sum equals the valence of Me except where Y is oxygen or sulphur, when the valency equals 2m + n, (e.g. Ti(O nC.sub.4 H.sub.9)Cl.sub.3), in a liquid reaction medium constituted by an aliphatic, aromatic, cycloaliphatic or halogenated hydrocarbon such as methyl chloride, and at a temperature in the range from -100.degree. to 30.degree.C.