PURPOSE: The titled catalyst component, consisting of a contact product of a specific contact product, acid halide compound and liquid titanium compound, having high activity, capable of giving polymers having good polymer properties and usable as a transition metal catalyst component of a Ziegler catalyst.

CONSTITUTION: A catalyst component consisting of a contact product of (A) a contact product of (i) a magnesium halide compound, e.g. MgCl2, (ii) an alkoxy group-containing compound of a metal selected from Groups IWIV of the periodic table, preferably tetraalkoxytitanium or tetraalkoxysilane, and (iii) an alcoholic compound, preferably 1W10C alcohol, (B) an acid halide com pound, e.g. ortho-C6H4(COCl)2 and, (C) a liquid titanium compound, e.g. TiCl4.