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We have studied the frequency and temperature dependences of permittivity and impedance of the compounds ACu3Ti4O12 (A=Ca, Bi2/3, Y2/3, Las2/3) in the ranges of 10−1–106 Hz and −150–200 °C. All compounds investigated display similar dielectric properties. Specifically, they all have a Debye-like relaxation and their dielectric constants are independent of frequency and temperature over a wide range. They all have two electrical responses in impedance formalism, indicating that there are two distinct contributions. We attribute them to grains and grain boundaries in the ceramic samples and explain the dielectric behaviors by Maxwell-Wagner relaxation arising at the interfaces between grains and their boundaries.