A resinous composition excellent in processability and gas permeation resistance, which comprises (A) 30 to 98% by weight of a crystalline polyolefin, (B) 2 to 70% by weight of a saponified product of an ethylene-vinyl acetate copolymer having an ethylene content of 25 to 75 mole % and a degree of saponification of at least 93%, and (C) 0.5 to 15 parts by weight, per 100 parts by weight of said polyolefin and ethylene-vinyl acetate copolymer saponified product, of a copolymer of maleic anhydride with other .alpha. ,.beta.-ethylenically unsaturated monomer free of a carbonyl group, said copolymer containing carbonyl groups in an amount of 120 to 1400 milliequivalents per 100 g of the polymer.