Abstract: Polyethylene and copolymers of predominant amounts of ethylene and minor amounts of comonomers which are polymerizable with ethylene are obtainable by free radical polymerization of the monomers under from 1,500 to 5,000 bar and at from 40.degree. to 250.degree. C. by means of an initiator with virtually complete exclusion of oxygen in not less than n=3 polymerization stages, by a method in which, in the first stage, the total amount of the predominant part of the monomers are subjected to polymerization using some of the initiator required, until said polymerization comes virtually to a stop, thereafter a further part of the initiator and, if required, of the monomers are added to the mixture, which has been cooled by 20.degree.-60.degree. C., and this process is repeated in the subsequent stages until the n th stage, with the proviso that the initiators used in the (n-1) th stage have a half-life temperature of from 80.degree. to 160.degree. C.