A catalyst system suitable for preparing substantially terminally unsaturated atactic polymers or copolymers of &agr;-olefins having a number average molecular weight in the range 300-500,000 comprises (A) a metallocene complex and (B) a cocatalyst comprising (i) a Group III Metal alkyl compound and (ii) a triaryl boron compound. Preferred metallocenes are those having alkyl ligands on the metal atom. The preferred Group III metal alkyl compound is triisobutyl aluminum and the preferred triaryl boron compounds is tris(pentafluorophenyl)boron.