PURPOSE: To obtain efficiently the title copolymer having excellent adhesiveness and compatibility, by copolymerizing ethylene, an α-olefin and a specified monomer in the presence of a catalyst consisting of a soluble V compd. and an org. Al compd. and a halogen-contg. metal compd.

CONSTITUTION: A mixture of ethylene (A), a 3W18C α-olefin (B) and a hydroxylated monomer (C) of formula I of II (wherein l is 1W3; R1 is a 2C or higher aliph. hydrocarbon group; p is 0 or 1; m and n are each 0W2; R2 is a direct bond or a 1C or higher aliph. hydrocarbon group; R3 is H or a 1W10C hydrocarbon group) is continuously copolymerized in the presence of a catalyst consisting of a soluble vanadium compd. and an org. aluminum compd. and 0.7W2mol of halogen-contg. metal compd. other than a halogenated org. aluminum compd. based on 1mol of component C in a hydrocarbon solvent to obtain the title copolymer.