A modified ethylenic random copolymer derived from 100 parts by weight of a base ethylenic random copolymer composed of 25 to 75 mole % of ethylene and 75 to 25 mole % of an alpha-olefin having 3 to 20 carbon atoms and grafted thereto, (a) 0.2 to 50 parts by weight of an unsaturated carboxylic acid having 3 to 10 carbon atoms or an anhydride or ester thereof, (b) 0.2 to 200 parts by weight of a styrene-type hydrocarbon having 8 to 12 carbon atoms, or (c) 0.2 to 300 parts by weight of an unsaturated silane compound having 2 to 20 carbon atoms, said modified ethylenic random copolymer having an intrinsic viscosity [.eta.], measured in decalin at 135.degree. C., of 0.01 to 1.5 dl/g and a molecular weight distribution (Mw/Mn), measured by gel permeation chromatography, of not more than 4.