A process for polymerizing 1-butene, optionally with up to 30% by mol of ethylene, propylene or an alpha olefin of formula CH2═CHT wherein T is a C3-C10, 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; R1, R2, R5, R6, R7, R8 and R9 are hydrogen atoms or hydrocarbon groups; with the proviso that at least one of R6 or R7 is a C1-C20 alkyl group; R3 and R4 are C1-C20 alkyl groups; and an alumoxane and/or a compound capable of forming an alkyl metallocene cation.