PURPOSE: To obtain a copolymer which is colored little and is excellent in clarity and resistance to water absorption by using an alkali metal-based catalyst in the initiation stage, subjecting the resultant arom. vinyl-conjugated diene copolymer to a specific deactivation treatment, and treating the copolymer with a specific compd.

CONSTITUTION: In the initial stage of the production, an alkali metal-based catalyst (Me) (e.g. n-butyllithium) is used. The resultant arom. vinyl-conjugated diene copolymer (e.g. a styrene-butadiene copolymer) is deactivated with an epoxy compd. (e.g. propylene oxide) to convert the terminal groups of the copolymer into alkali metal alcoholate groups (-O-Me). The copolymer is then treated with at least one polycarboxylic acid cyclic anhydride (e.g. 1,2,4- benzenetricarboxylic anhydride), e.g. by adding the anhydride to the polymn. soln.