A saponified ethylene-vinyl acetate resin, containing from 0.1 to 3000 ppm of a compound having a molecular weight of at most 1000 and having at least one conjugated double bond, an alkoxy group content of from 0.0005 to 1 mol %, an ethylene content of from 5 to 60 mol %, and a degree of saponification of at least 85 mol % has good melt extrusion stability, drawdown resistance, interlayer adhesion and gas barrier properties, and products made therefrom have good surface smoothness. The saponified ethylene-vinyl acetate resin may be produced by polymerizing a mixture of ethylene and vinyl acetate in the presence of a polymerization initiator having an alkoxy group, thereby producing an ethylene-vinyl acetate copolymer, adding a compound having a molecular weight of at most 1000 and at least one conjugated double bond to the ethylene-vinyl acetate copolymer, then saponifying the ethylene-vinyl acetate copolymer, thereby forming a saponified ethylene-vinyl acetate copolymer.