A process for producing a polymer of ethylene containing from 0.1 to 50% by weight of one or more derived units of alpha-olefins fo formula CH.sub.2.dbd.CHR, wherein R is a C.sub.2-C.sub.20 alkyl radical, comprising contacting, under polymerization conditions, ethylene and one or more alpha-olefins in the presence of a catalyst system obtainable by contacting: a) a metallocene compound of formula (I) wherein: M is zirconium titanium or hafminum, X, equal to or different from each other, is hydrogen halogen or an hydrocarbyl radical, R.sup.1, R.sup.2, R.sup.3, R.sup.4, R.sup.5, R.sup.6, R.sup.7, R.sup.8 and R.sup.9, equal to or different from each other are hydrogen atoms, halogen atoms, or hydrocarbyl radicals; and b) an alumoxane or a compound capable of forming an alkyl metallocene cation. ##STR00001##