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A nanocrystalline Cr-doped ZnO has been prepared by refluxing method. The samples were characterized using XRD and impedance spectroscopy. The XRD pattern shows the crystalline nature of the sample and well confirms the successful doping Cr into the host lattice. The conductivity of the sample measured in the temperature range 303-603K and in the frequency range 10Hz-1MHz. The temperature dependent dc conductivity and hopping frequency show Arrhenius behavior. AC conductivity data were analyzed using Jonscher's power law. Modulus data were analyzed using Bergman modified KWW function. Temperature dependent capacitance shows a sharp peak at 540K which may be due to ferroelectric nature of the material. [ABSTRACT FROM AUTHOR]