The results of thermally stimulated discharging currents and isothermal direct currents measurements, performed on crosslinked polyethylene cable models aged under different thermal and electrothermal stresses, are presented and discussed. It is shown that aging affects the low-frequency behavior of the polymer. The changes observed in the relaxation processes are related to those of other properties, e.g., density, melting enthalpy, electric strength, electrical conductivity, and microstructure, as well as to the degradation phenomena caused in the insulation by the applied stresses. The proposed techniques, therefore, prove to be an effective diagnostic tool for investigating the aging of polymeric insulating materials.