Abstract: A process for preparing an olefin polymer or copolymer by polymerizing or copolymerizing an olefin containing at least 3 carbon atoms which may contain at most 10 mole % of ethylene and/or a diene, in the presence of a catalyst composed of (A) a solid titanium catalyst component prepared by(1) reacting a mechanically pulverized product of an organic acid ester and a halogen-containing magnesium compound, with an active hydrogen-containing organic compound in the absence of mechanical pulverization,(2) reacting the resulting reaction product with an organometallic compound of a metal of Groups I to III of the periodic table in the absence of mechanical pulverization, and(3) washing the resulting solid reaction product with an inert organic solvent, reacting the washed solid reaction product with a titanium compound in the absence of mechanical pulverization, and separating the solid from the reaction system,and (B) an organometallic compound of a metal of Groups I to III of the periodic table; and a catalyst u