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This paper focuses on accelerated testing procedures that can be applied to XLPE and EPR for high voltage cables and that are aimed to achieve the thermo-electrical endurance characterization of insulation. Several methods and techniques for single and combined thermo-electrical stress are illustrated; indices for the evaluation of electrical, thermal, and multi-stress endurance are reported and their derivation is shown. Indications on the feasibility of the design-stress inference from tests on laboratory specimens also are given. Experimental results mainly refer to cable models, but data relevant to full-sized cables, as well as to simple, flat specimens, are also considered.