A copolymer of 30-90 mol % ethylene und an alpha-olefine having 3 to 14 carbon atoms, with a number average molecular weight of 300-30000, a Q value of not more than 3 and a Z value of 15-200, is prepared in a continuous way in the presence of hydrogen and of a vanadium compound with the formula VO(OR )n X 3-n or VX 4 [R : aliphatic hydrocarbon group having 1 to 20 carbon atoms; X : halogen atom; n: number from 0 to 3] and an organo-aluminium compound with the formula R mAl X 3-m [R : aliphatic hydrocarbon group having 1 to 6 carbon atoms; X : halogen atom; m: number from 1 to 3]. The copolymer is used as a synthetic lubricant oil or fuel oil component.