A process for polymerizing I-butene comprising the step of contacting under polymerization "conditions 1-butene and optionally from 0 to 20% by mol of an alpha olefin with a catalyst system obtainable by contacting a bridged metallocene compound of formula (I) wherein R.sup.1 and R.sup.2 are an hydrocarbon radical A is a carbon atom, a germanium atom or a silicon atom; m is 1, 2; M is a metal of group 4 of the Periodic Table of the Elements; X, is hydrogen, a halogen atom, or a group R, OR, OS0.sub.2CF.sub.2, OCOR, SR, NR.sub.2 or PR.sub.2, wherein the substituents R are hydrocarbon radical; L is a moiety of formula (IIa), (IIb), or (IIc) wherein T is an oxygen (0) or sulphur (S) atom or a CH2 group; and R.sup.3, R.sup.4, R.sup.5, R.sup.6, R.sup.7, R.sup.8 are hydrogen or hydrocarbon radicals; one or more alumoxanes or compounds able to form an alkylmetallocene cation; and optionally an organo aluminum compound.