Process for producing graft-modified alpha-olefin copolymer

The process for producing a graft-modified .alpha.-olefin copolymer, which comprises the following steps (a) and (b):

• Step (a) which is a step of copolymerizing, with the use of a Ziegler-Natta catalyst comprising a transition metal compound and an organometal compound, an .alpha.-olefin having 2 to 20 carbon atoms with a dialkenylbenzene represented by the formula:
• ##STR7## wherein, R.sup.1 represents a hydrogen atom or a methyl group, R.sup.2 represents a hydrocarbyl group having 1 to 6 carbon atoms and n represents 0 or 1, thereby to prepare a random copolymer of the .alpha.-olefin with the dialkenylbenzene such that a first alkenyl group is utilized in the copolymerization with a second alkenyl group in the dialkenylbenzene remaining unpolymerized, the amount of the dialkenylbenzene in the copolymer being in an amount of 0.001 to 10% by weight;
• and
• Step (b) which is a step of graft-polymerizing, with the use of an anion-polymerization initiator, an anionically polymerizable monomer which is styrene onto said copolymer obtained in the step (a), said anion-polymerization initiator being selected from the group consisting of organometallic compounds having a metal-carbon bond of an alkali metal or an alkaline earth metal, the step (b) being conducted by adding the catalyst after the addition of styrene to the copolymer in the step (a), thereby to produce a graft copolymer such that styrene has been polymerized onto the unpolymerized alkenyl group on the copolymer prepared in the step (a).