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Water treeing is one of the factors leading to failure of medium voltage XLPE cables in long-term service. Increased moisture content inside oil-paper insulated cable is not desirable. To identify water tree degraded XLPE cables or oil-paper cables with high moisture content, diagnostic tests based on dielectric response (DR) measurement in time and frequency domain are used. Review of individual DR measurement techniques in the time and frequency domains indicates that measurement of one parameter in either domain may not be sufficient to reveal the status of the cable insulation. But a combination of several DR parameters can improve diagnostic results with respect to water trees present in XLPE cables or increased moisture content in oil-paper cables. DR measurement is a very useful tool that reveals average condition of cable systems. However, it is unlikely that DR measurement will detect few, but long water trees. In addition, DR cannot locate the defect or water tree site within the cable system. Combination of DR and partial discharge (PD) measurements can improve diagnostic results with respect to global and local defects. However, it is doubtful whether PD test can identify the presence of water trees inside a cable in a nondestructive manner. Further research is needed for more detailed conclusions regarding the status of a particular insulation and for predicting the remaining life of the insulation system.