In a process for producing a polymer or copolymer of an alpha-olefin which comprises continuously polymerizing or copolymerizing the alpha-olefin or the alpha-olefin with up to 5 mole % of a diolefin in the presence of a catalyst comprising a transition metal catalyst component and an organoaluminum catalyst component, the improvement wherein:(I) said polymerization or copolymerization is carried out in the presence of a catalyst composed of (A) a solid magnesium compound obtained by reacting (i) an adduct between a magnesium halide and an electron donor, with (ii) an organometallic compound of a metal of Groups I to III of the Mendelejeff's periodic table, (B) a liquid transition metal compound, and (C) an organoaluminum compound, and(II) said continuous polymerization or copolymerization is carried out while feeding the compound (B) separately from the other compounds (A) and (C) into a polymerization or copolymerization zone.