A cyclic olefin addition copolymer includes a structural unit (1) derived from a cyclic olefin compound with a C4 alkyl substituent group and a structural unit (2) derived from a cyclic olefin compound with a C5-12 alkyl substituent group, and optionally includes a structural unit (3) derived from another cyclic olefin compound. The novel cyclic olefin addition copolymers according to the present invention are excellent in melt-formability, transparency and heat resistance, have low water absorption properties, low dielectric constant and low metal content, and are suitably used in optical parts such as optical films. Processes according to the present invention produce the cyclic olefin addition copolymers at high yield with small amounts of catalysts.