A hydrolyzed ethylene-vinyl acetate copolymer having an ethylene content of 20 to 60% by mole and a defree of hydrolysis in the vinyl acetate component of at least 95% by mole, having an ash content of not more than 20 ppm and an alkali metal content of not more than 5 ppm, and having a ratio of the melt viscosity at 220 DEG C. after maintaining the copolymer at 220 DEG C. for 60 minutes to the melt viscosity at 220 DEG C. after maintaining the copolymer at 220 DEG C. for 5 minutes of 1.0 to 1.5. The hydrolyzed copolymer of the invention can give the films whose gas impermeability is not lowered even at high humidity, and is applicable to long-run molding.
