A cyclic olefin addition copolymer obtained by copolymerizing a cyclic olefin compound having a side chain substituent group with a ring structure, such as endo-tricyclo[4.3.0.1^2,5]deca-3,7-diene or endo-tricyclo[4.3.0.1^2,5]deca-3-ene, with another cyclic olefin compound such as bicyclo[2.2.1]hept-2-ene, and further with a cyclic olefin compound having a hydrolysable silyl group as needed, or hydrogenating after copolymerization; a composition for crosslinking in which a specific crosslinking agent is incorporated; a crosslinked product obtained by crosslinking the composition; an optical material containing the copolymer, the composition or the crosslinked product; and a method for producing the copolymer in which addition polymerization is conducted using a specific nickel catalyst.