Catalyst composition and process for polymerizing olefins

A process for producing an olefin polymer or copolymer which comprises polymerizing or copolymerizing olefins or copolymerizing an olefin with up to 5 mole% of a diolefin in the presence of a catalyst comprising a titanium catalyst component containing magnesium, titanium, halogen and an electron donor, an organoaluminum catalyst component and a third catalyst component, characterized in that said catalyst is composed of (A) a titanium catalyst component containing magnesium, titanium, halogen and an electron donor as essential ingredients, said electron donor being selected from the group consisting of (a) esters of polyfunctional compounds selected from polycarboxylic acids having 5 to 36 carbon atoms, polyhydroxy compounds having 6 to 28 carbon atoms and hydroxy-substituted carboxylic acids having 10 to 28 carbon atoms,(b) monocarboxylic acid esters of the formula RCOOR' in which each of R and R' represents a hydrocarbyl group having 1 to 20 carbon atoms, and at least one of them represents a branched-chain group, an alicyclic group, or an aryl ring-containing linear group, and(c) carbonic acid esters having 3 to 18 carbon atoms,(B) an organoaluminum compound, and (C) an ester of phosphorous acid with an alcohol having 2 to 4 carbon atoms; and a catalyst composition used therefor.