the present invention discloses an alkylidenenorbornene polymer comprising as the essential constituent at least one kind of the structural unit represented by the formula ## str1 ## wherein r 1 denotes an alkyl group of 1 - 4 carbon atoms and r 2 denotes a hydrogen atom or an alkyl group of 1 - 5 carbon atoms , and a process for producing the same . according to the present invention , an alkylidenenorbornene polymer is obtained which is excellent in light resistance , transparency , heat resistance and moisture resistance and is useful as an optical polymeric material .