Catalyst system suitable for preparing substantially terminally unsaturated atactic polymers or copolymers of &agr;-olefins having a molecular weight (Mn) in the range 200-500,000. The catalyst system includes a metallocene of the formula: [RmCpH(5-m)][RnCpH(5-n)]M(Z)Y wherein CpH is a cyclopentadienyl ligand, each R represents an alkyl or an aryl substituent on the CpH ligand or two R's may be joined together to form a ring, or the Rs in each CpH group when taken together represents an Si or C bridging group linking two CpH groups wherein the Si or C group may itself be substituted by hydrogen atoms or C1-C3 alkyl groups, M is a metal selected from hafnium, zirconium and titanium, Z is selected from a hydrogen atom, a trifluoromethane sulphonate, an alkyl and an aryl group, Y is selected from a, 1,3-diketonate and a &bgr;-ketoester arion, and each of m and n is same or different and has a value from 0 to 5.