PURPOSE: To obtain efficiently polymers excellent in flexural elastic modulus, etc., by using 2,6-dihalo-4-alkylphenol as phenolic compounds to be used for metathesis polymerization having strained rings.

CONSTITUTION: The cycloolefin polymer is obtained by mixing metathesis polymer catalyst (ex.: tungsten catalyst) with 2,6-dihalo-4-1C to 4C alkylphenol (ex.:2,6-dibromo-4-methylphenol). Then, by contacting this reaction mixture with metathesis catalyst activators such as alkyl aluminum halide, etc., containing 1C to 10C alkyl groups and cycloolefin, with at least one type of cycloolefin (ex.: cyclopentadiene) having strained rings in the molar ratio range of cycloolefin: tungsten of about (1000-15000):1 at a temperature of about 30 to 100°C.