This invention provides an ethylene-vinyl alcohol copolymer composition having specific flow characteristics in the relationship between the heating time and the extrusion rate measured with a capillary rheometer (Koka Flow Tester), and a multilayered structure utilizing the same.From the EVOH composition according to the present invention, can be obtained a molded article, particularly a multilayered structure, having an excellent appearance; more particularly, in a continuous melt molding operation over a long period, a molded article, particularly a multilayered structure, having an excellent appearance can always be obtained without worsening the appearance with running time.