A process for preparing ethylene polymers by the high-pressure method comprises dissolving one or more free-radical initiators in one or more ketones of the formula I ##STR1##

where R¹ and R² are identical or different and are selected from among C₁-C₆-alkyl and C₃-C₁₂-cycloalkyl and R¹ and R² may also be covalently linked to one another to form a 4- to 13-membered ring, prior to the polymerization,

compressing the solution, metering it into the polymerization reactor at one or more points and subsequently carrying out the polymerization at from 150 to 380 C. and from 500 to 4500 bar.