NOVELTY - A polymer composition contains crystalline norbornene type ring-opened polymer which is obtained by hydrogenating ring opened polymer, and noncrystalline alicyclic structure containing polymer in which glass transition temperature is greater than or equal to 50 degrees C and does not have melting point in ratio of 90/10-50/50 (weight ratio).    USE - A polymer composition for film (claimed) used for foodstuff field such as food packaging bags, medical field such as bag for infusion solutions, energy field such as solar energy power generation system edge strip, display field such as barrier film, optical field, electric electronic field, telecommunications sector, motor vehicle field, consumer application field, and civil engineering and construction field.    ADVANTAGE - The composition provides film which reconciled transparency and low water-vapor permeability.    DETAILED DESCRIPTION - A polymer composition contains crystalline norbornene type ring-opened polymer which is obtained by hydrogenating ring opened polymer, and noncrystalline alicyclic structure containing polymer in which glass transition temperature is greater than or equal to 50 degrees C and does not have melting point in ratio of 90/10-50/50 (weight ratio). The crystalline norbornene type ring-opened polymer has melting point of 110-145 degrees C, weight average molecular weights of 50000-200000 measured by gel permeation chromatography, and weight average molecular weight/number average molecular weight of 1.5-10. The polymerizable monomer is formed by containing 90-100 wt.% of 2-norbornenes and 10-0 wt.% of substituent containing norbornene, and carries out ring-opening polymerization. The total amounts of 2-norbornene compound and dicyclopentadiene compound are greater than or equal to 90 wt.% and 100 wt.%. The 2-norbornene compound weight is obtained from polymerizable monomer which is less than or equal to one half of dicyclopentadiene compound weight. An INDEPENDENT CLAIM is included for a film containing polymer composition. The film has water vapor permeability of less than or equal to 20% and haze of not greater than 0.40 g/m2x day when thickness is 100 mu m.