Process for polymerizing or copolymerizing ethylenically unsaturated monomers in the presence of free-radical polymerization initiators at pressures in the range of from 110 MPa to 500 MPa and temperatures in the range of from 100° C. to 350° C. in a continuously operated polymerization apparatus, wherein the reaction gas composition is compressed to the polymerization pressure by at least two sequentially operating compressors in which a low-pressure compressor first compresses the reaction gas composition to a pressure of from 10 MPa to 50 MPa and a high-pressure compressor then further compresses the reaction gas composition to the polymerization pressure wherein the high-pressure compressor is operated with a polyalkylene glycol based synthetic lubricant and oxygen is introduced into the fresh gas feed or into the polymerization apparatus in an amount that the gas composition to be compressed in the high-pressure compressor has an oxygen content in the range of from 0.01 ppm to 0.9 ppm.