The invention provides an adhesive composition comprising a specific grafted long-chain branched ethylene- alpha -olefin copolymer and either a tackifier or a specific ethylene-vinyl acetate copolymer, wherein the density, MFR, crystallinity and graft ratio thereof lie respectively within specific ranges. Such a composition containing a tackifier can give a laminate keeping an excellent adhesive strength even in a high-temperature atmosphere together with polystyrene resin, ABS resin, polyacrylonitrile resin or saponified ethylene-vinyl acetate copolymer resin, while such a composition containing an ethylene-vinyl acetate copolymer can give such a laminate together with polyester resin, polycarbonate resin, polyvinylidene chloride resin or saponified ethylene-vinyl acetate copolymer resin. The invention also provides another adhesive composition comprising a grafted long-chain ethylene- alpha -olefin copolymer and an olefinic elastomer. This composition can provide a film layer excellent in adhesion to metals or highly polar materials.