A process for producing an ethylene copolymer having a density of from 0.900 to 0.945 g/cm.sup.3 by copolymerizing in two steps a predominant amount of ethylene with a minor amount of an alpha-olefin containing at least 3 carbon atoms at room temperature to not more than about 100.degree. C. under a pressure of about 1 to about 100 kg/cm.sup.2 in the presence of a catalyst composed of (A) a titanium catalyst component supported on a magnesium compound and (B) an organoaluminum compound; characterized in that said copolymerization is carried out in(i) a first step where about 0.01 to about 50 g, per gram of the titanium catalyst component (A), of the alpha-olefin containing at least 3 carbon atoms is polymerized, said catalyst further comprising an organic acid ester (C), and then(ii) a second step where the final product of ethylene copolymer is formed in an amount more than about 100 times the weight of the polymer formed in the first step.