Ethylene homopolymers and copolymers are prepared in a tube reactor at from 160° C. to 350° C. and pressures in the range from 500 to 5000 bar, with or without use of molar mass regulators, using a peroxide mixture comprising from 1 to 95 mol %, based on the total amount of the peroxide mixture, of at least one cyclic peroxide of the formula I, where the radicals R are identical or different and are selected from among alkyl groups and aryl groups, as polymerization initiator.