An ethylene-vinyl alcohol copolymer composition excellent in neck-in reduction, stretching properties and further, gas barrier properties and a multilayer structure using the same, are disclosed. The ethylene-vinyl alcohol copolymer composition of the present invention is the blend of two or more ethylene-vinyl alcohol copolymers and at least one of the copolymers has the following structural unit (1). (wherein X represents any binding chain excluding an ether bond, each of R1 to R4 represents independently any substituent and n represents 0 or 1). Preferably, the ethylene-vinyl alcohol copolymer having the structural unit (1) is obtained by hydrolyzing of a copolymer of 3,4-diacyloxy-1-butene, a vinyl ester monomer and ethylene.