To provide a novel cross
copolymer and resin composition which are improved in
heat resistance and compatibility over conventional
ethylene / aromatic vinyl compound copolymers and which have low
crystallinity, are excellent in softness, transparency and compatibility and show mechanical properties similar to soft
vinyl chloride resins, as compared with conventional cross copolymers.A process for producing a cross
copolymer, which comprises a
coordination polymerization step and a subsequent anionic
polymerization step, wherein in the
coordination polymerization step, copolymerization of an olefin
monomer, an aromatic vinyl compound
monomer and an aromatic
polyene is carried out by using a single-site
coordination polymerization catalyst to synthesize an olefin / aromatic vinyl compound / aromatic
polyene copolymer, and then, in the anionic
polymerization step,
polymerization is carried out in the coexistence of such an olefin / aromatic vinyl compound / aromatic
polyene copolymer and an anionic polymerizable vinyl compound
monomer by using an anionic polymerization initiator.