A process for polymerizing or copolymerizing ethylenically unsaturated monomers in the presence of free-radical polymerization initiators, wherein the polymerization is carried out at temperatures from 100° C. to 350° C. and pressures in the range of from 110 MPa to 500 MPa in a continuously operated polymerization reactor which is controlled by a pressure control valve at the outlet of the polymerization reactor, the process comprising continuously monitoring the pressure within the polymerization reactor, feeding a pressure signal to a controller for controlling the control valve and having the controller altering the opening of the pressure control valve to control the pressure within the polymerization reactor, wherein the controller starts an emergency shutdown program when the pressure control valve closes more than a preset threshold value and the pressure within the polymerization reactor decreases below a preset pressure threshold.