A process for the preparation of 1-butene homopolymers or 1-butene/alpha olefin copolymers wherein the alpha olefins are selected from ethylene, propylene or alpha olefins of formula CH2═CHZ wherein Z is a C3-C20 alkyl radical, comprising contacting 1-butene or 1-butene and one or more alpha olefins under polymerization conditions in the presence of a catalyst system comprising: (a) a solid component comprising a Ti compound and an internal electron-donor compound supported on MgCl2 (b) an alkylaluminum cocatalyst; and (c) a compound of formula (I) as external donor Wherein: R1, R2, R3 and R4, equal to or different from each other, are hydrogen atoms or C1-C20 hydrocarbon radicals optionally containing heteroatoms belonging to groups 13-17 of the Periodic Table of the Elements; or two R1, R2, R3 and R4 can be joined to form a C5-C20, saturated or unsaturated ring.