the process , which comprises a first stage for polymerizing ethylene at 180 °- 320 ° c . and 300 - 2 , 500 bars in the presence of a ziegler type catalytic system , a second stage for separation , a third stage for recycling unreacted monomers , and a fourth , recompression stage , is characterized by introducing into the stream of recycled monomer during the third stage , at least one compound selected from the amides of the saturated or unsaturated organic acids containing from 12 to 22 carbon atoms , polyalkylene polyols containing from 4 to 500 carbon atoms , and compounds containing at least two epoxide functions , with a molecular weight greater than approximately 200 . preferably from 0 . 005 to 0 . 1 mole of the selected compound is introduced per ton of recycled monomer . this process makes it possible to avoid the formation of high molecular weight polymers in the recycle circuits .