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 having C1 symmetry with an alumoxane and/or a compound capable of forming an alkyl metallocene cation.