PURPOSE: To obtain a low-density, low-MI copolymer and, at the ame time, to decrease the amount of expensive 5C or higher olefins, by copolymerizing ethylene and α-olefin first by a solution process and then by a vapor phase process while selecting the kinf of the olefin used.

CONSTITUTION: In the copolymerization of ethylene and α-olefins in the presence of a catlyst consisting of (A) a solid catalytic component containing Mg, Ti and a halogen and (B) an organometallic compound component, ethylene and about 1W250mol%, based on ethylene 5W15C olefins (e.g., 4-methyl-1-pentene) are copolymerized at 0W120°C in the presence of a hydrocarbon solvent to form a copolymer in an amount of 1W70wt% based on total weight of the final copolymer, then the solvent is removed from the resulting copolymer (density about 0.925W 0.955) and, if necessary, an organometallic compound component is added and ethylene and about 1W250mol%, based on ethylene, 3W4C olefin (e.g., 1-butene) are fed and copolymerized in a vapor phase at about 20W110°C.