A modified aluminum oxy compound (A) obtained by reacting an aluminum oxy compound
(a), water (b) and a compound having a hydroxyl group (c); a polymerization catalyst
component comprising the modified aluminum oxy compound; a polymerization catalyst
obtained by contacting said modified aluminum oxy compound (A), a transition metal
compound (B) and optionally an organoaluminum compound (C) and a specified boron
compound; and a process for producing an olefin polymer or an alkenyl aromatic
hydrocarbon polymer with the polymerization catalyst.
