NOVELTY - An ethylene monomer, aromatic vinyl compound monomer and aromatic polyene are copolymerized at 80-150 degrees C using single-site coordination-polymerization catalyst comprising transition metal compound (1) and co-catalyst, to form ethylene-aromatic vinyl compound-aromatic polyene copolymer. The ethylene-aromatic vinyl compound-aromatic polyene copolymer and anion polymerization property vinyl compound monomer are polymerized in presence of anionic initiator, to obtain cross copolymer.    USE - Manufacture of cross-copolymer for resin composition used for forming molded products such as film and sheet, tape base material, tube, foamed material and wire-coating material (all claimed). Uses include but are not limited to building materials for floor and wall, interior-and-exterior cladding material for motor vehicles, gasket, shock absorbing material, film for packaging, shrink film, dicing film for electronic materials, bag, pouch, and adhesive tape used as protection tape, sealing tape, fixing tape, dicing tape and binding tape.    ADVANTAGE - The method provides cross-copolymer having excellent heat resistance, compatibility, transparency and elastic recoverability, and reduced film anisotropy.    DETAILED DESCRIPTION - An ethylene monomer, aromatic vinyl compound monomer and aromatic polyene are copolymerized at 80-150 degrees C using single-site coordination-polymerization catalyst comprising transition metal compound of formula (1) and co-catalyst, to form ethylene-aromatic vinyl compound-aromatic polyene copolymer having aromatic vinyl compound unit content of 5-15 mol%, aromatic polyene unit content of 0.01-3 mol% and remainder of ethylene unit content. The ethylene-aromatic vinyl compound-aromatic polyene copolymer and anion polymerization property vinyl compound monomer are polymerized in presence of anionic initiator, to obtain cross copolymer.    A,B'=(un)substituted benzoindenyl group of formula (2, 3 or 4) or (un)substituted indenyl group of formula (5);    R1-R4=H, 1-20C alkyl, 6-10C aryl, 7-20C alkylaryl, halo, OSiR3, SiR3 or PR2, where adjacent R1, R2 are optionally adjoined together to form 5-8 membered aromatic ring or aliphatic ring;    Y'=H, methylene group having 1-15C hydrocarbon (optionally including nitrogen, oxygen, sulfur, phosphorus and/or silicon) as substituent, or boron group;    X=H, hydroxyl, halo, 1-20C hydrocarbon, 1-20C alkoxy, silyl having 1-4C hydrocarbon substituent, or amide having 1-20C hydrocarbon substituent, where two X are optionally combined;and    M=zirconium, hafnium or titanium.