A PROCESS FOR THE PRODUCTION OF WAXY, LOW MOLECULAR WEIGHT POLYETHYLENES IN WHICH ETHYLENE IS POLYMERIZED UNDER THE ACTION OF A POLYMERIZATION INITIATOR WHICH FORMS FREE RADICALS AND IN THE PRESENCE OF A POLYMERIZATION REGULATOR AT ELEVATED TEMPERATURE AND AT SUPERATMOSPHERIC PRESSURE. IT IS A CHARACTERISTIC OF THE PROCESS ACCORDING TO THE INVENTION THAT AS THE FREE RADICAL-FORMING POLYMERIZATION INITIATOR THERE ARE JOINTLY USED: (1) A SPECIFIC AMOUNT OF AN ORGANIC PEROXIDE HAVING A HALF-LIFE TEMPERATURE OF FROM 60* TO 112*C., AND (2) A SPECIFIC AMOUNT OF OXYGEN. HIGH YIELDS CAN BE OBTAINED BY THE PROCESS AND A PRODUCT CAN BE OBTAINED WHICH HAS PARTICULARLY GOOD OIL-BINDING PROPERTIES.