Abstract: A method of copolymerization in suspension of ethylene with straight-chain alpha-olefins so as to obtain low-density copolymers in two copolymerization steps in an aliphatic hydrocarbon medium having a boiling point above 40.degree. C. In the first reaction step the medium is supplied with a high-activity Ziegler catalyst on a carrier and with ethylene and the alpha-olefin. The copolymerization reaction is carried out for between 20 seconds and 30 minutes and at a temperature between 45.degree. and 65.degree.. The resulting copolymer is used in the second reaction step as a nucleus for polymerizing ethylene and the alpha-olefin, the reaction medium being supplied with additional quantities of ethylene and alpha-olefins so as to maintain the concentration of alpha-olefin in the reaction medium at between 4 and 25% by weight per 100 parts by weight of reaction medium and so as to maintain the pressure of ethylene at between 5 and 25 bars, the reaction being performed at a temperature between 50.degree. and 80.