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 having C.sub.1 symmetry with an alumoxane and/or a compound capable of forming an alkyl metallocene cation.