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We studied frequency and temperature dependences of impedance, electric modulus, and dielectric permittivity of Bi2/3Cu3Ti4O12 in the ranges of 10−1–106 Hz and −150–200 °C, respectively. We first observed two electrical responses in the impedance and modulus formalisms. Then we detected a Debye-like relaxation in the permittivity formalism. Most interestingly, we found that the large dielectric constant of Bi2/3Cu3Ti4O12 is independent of the temperature and frequency below 150°C. The results are interpreted in terms of a two-layer model with conducting grains partitioned from each other by poorly conducting grain boundaries. Using this model, we attributed the two electrical responses in impedance and modulus formalisms to the grain and grain-boundary effects, respectively, while the detected Debye-like relaxation and large dielectric constant were well explained in terms of Maxwell-Wagner relaxation.