Process for the polymerization of olefins comprising contacting olefins under polymerization conditions in the presence of a catalyst system comprising the product obtained by contacting: (A) at least one transition metal organometallic compound, pyrolidyl bis(η-cyclopentadienyl)methylzirconium being excluded, and (B) an organometallic compound obtained by contacting: (a) a Lewis base having formula (I):  wherein Ra, Rb, Rc and Rd, equal to or different from each other, are selected from the group consisting of hydrogen, halogen, linear or branched, saturated or unsaturated, C1-C10 alkyl, C6-C20 aryl, C7-C20 arylalkyl and C7-C20 alkylaryl groups; with b) a Lewis acid of formula (II) MtR13  (II)  wherein Mt is a metal belonging to Group 13 of the Periodic Table of the Elements; R1, equal to or different from each other, are selected from the group consisting of halogen, halogenated C6-C20 aryl and halogenated C7-C20 alkylaryl groups; and (C) optionally an alkylating agent.