A process for producing a copolymer of ethylene containing from 0.1 to 99% by mol of one or more derived units of alpha-olefins of formula CH.sub.2.dbd.CHA, wherein A 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 hafnium; X, same or different, is a hydrogen atom, a halogen atom, or an hydrocarbon group; R.sup.1, is a hydrocarbon group; R.sup.2 R.sup.3, R.sup.4, R5 and R.sup.6, are hydrogen atoms or hydrocarbon groups; Q is a radical of formula (II), being bonded to the indenyl at the position marked by the symbol *; (II) wherein: T.sup.1, T.sup.2, T.sup.3, T.sup.4 and T.sup.5, are carbon atoms (C) or nitrogen atoms (N); m.sup.1, m.sup.2, m.sup.3, m.sup.4 and m.sup.5 are 0 or 1; R.sup.7, R.sup.8, R.sup.9, R.sup.10 and R.sup.11 are hydrogen atoms or hydrocarbon groups; and b) an alumoxane or a compound capable of forming an alkyl metallocene cation. ##STR00001##