Disclosed is a specific adhesive polyethylene composition comprising [1] a modified ethylene/&agr;-olefin copolymer resin or elastomer obtained by modifying a specific ethylene/&agr;-olefin copolymer resin or elastomer, each of which comprises ethylene and an &agr;-olefin of 3 to 20 carbon atoms, with an unsaturated carboxylic acid or anhydride, ester, amide, imide or metallic salt derivative of a unsaturated carboxylic acid thereof, [2] an unmodified ethylene/&agr;-olefin copolymer resin and/or an unmodified ethylene/&agr;-olefin copolymer elastomer and [3] a tackifier. Also disclosed is a multi-layer laminated film of 3 or more layers in which a layer of the above composition is interposed between an ethylene polymer layer and either a polyamide resin layer, an ethylene/vinyl alcohol copolymer layer or a layer of a mixture of polyamide resin and ethylene/vinyl alcohol copolymer. The adhesive polyethylene composition shows excellent adhesion strength to ethylene polymers, polyamide resins and ethylene/vinyl alcohol copolymers, high heat-sealing strength and heat resistance. The multi-layer laminated film shows excellent strength, heat resistance and gas barrier properties, and besides this film has heat shrinkability, so that the film is suitably used as a shrink film.