Process for monitoring the polymerization of ethylene or ethylene and comonomers in the presence of free-radical polymerization initiator at pressures in the range of from 160 MPa to 350 MPa and temperatures in the range of from 100° C. to 350° C. in a tubular reactor with one or more reaction zones, which is equipped with cooling jackets for cooling the tubular reactor with a cooling medium, comprising the steps of a) measuring as process parameters the temperature profile and the pressure of the reaction medium and the flow and temperature profile of the cooling medium along the reactor, b) monitoring the feeds of ethylene, if present comonomer, free-radical polymerization initiator and chain-transfer agent to all reaction zones, c) calculating, based on the measured process parameters and on a model for the polymerization process, concentrations for free-radical polymerization initiator, chain-transfer agent, ethylene and, if present, comonomers at at least so many positions along the reactor, that at least one calculation is carried out all 10 s for a volume unit flowing through the reactor, d) calculating, based on the measured process parameters and the calculated concentrations, the cooling power, the generation of heat, and the concentration of radicals, e) calculating, based on the calculated data of the cooling power, of the generation of heat, and of the concentration of radicals, the potential of a thermal runaway of the reaction mixture at the positions along the reactor which have the highest temperatures, and f) outputting an alarm signal if the calculated value for the potential of a thermal runaway exceeds a predefined value and process for polymerizing ethylene or ethylene and comonomers comprising such a monitoring process.