A process for polymerizing 1-butene, optionally with up to 30% by mol of ethylene, propylene or an alpha olefin of formula CH.sub.2.dbd.CHT wherein T is a C.sub.3-C.sub.10 alkyl group, in the presence of a catalyst system obtainable by contacting a metallocene compound of formula (I) Wherein M is an atom of a transition metal; X is a hydrogen atom, a halogen atoms or a hydrocarbon group; R.sup.1, R.sup.2, R.sup.5, R.sup.6, R.sup.7, R.sup.8 and R.sup.9 are hydrogen atoms or hydrocarbon groups; with the proviso that at least one of R.sup.6 or R.sup.7 is a C.sub.1-C.sub.20 alkyl group; R.sup.3 and R.sup.4 are C.sub.1-C.sub.20 alkyl groups; and an alumoxane and/or a compound capable of forming an alkyl metallocene cation ##STR00001##