An ethylene-.alpha.-olefin copolymer comprising ethylene and an .alpha.-olefin having from 3 to 10 carbon atoms, the copolymer having an .alpha.-olefin content of from 1.0 to 8.0 mol %, a density of from 0.900 to 0.930 g/cm.sup.3, and a melt flow rate of from 0.1 to 100 g/10 min., the programed-temperature thermogram of said copolymer as determined with a differential scanning calorimeter after being completely melted and then gradually cooled showing an endothermic peak (a) in a range of from 75.degree. to 100.degree. C. and an endothermic peak (b) in a range of from 120.degree. to 140.degree. C., with the ratio of an endotherm at the endothermic peak (b), .DELTA.Hb, to an endotherm at the endothermic peak (a), .DELTA.Ha, i.e., .DELTA.Hb/.DELTA.Ha, being from 0.03 to 2.0. The copolymer provides a film exhibiting excellent physical properties required for packaging film.