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Cd2Nb2O7 is still an interesting ferroelectric material because of its high permittivity value at helium temperatures and a variety of dielectric relaxation processes, the origin of which is still puzzling. We prepared hot-pressed ceramics, with grain sizes from 100 to 150 nm, obtained from Cd2Nb2O7 nanopowders synthesized by high-energy milling of CdO and Nb2O5 and studied their dielectric response and thermal properties. The nanoceramics were characterized by X-ray diffraction and their dielectric properties were measured at temperatures from 4K to 575K. Dielectric response of the nanoceramics was found to consist of a huge anomaly at ~150K with complex dielectric absorption and three relaxation processes apparent in frequency and temperature dependences of the imaginary part of permittivity in the temperature range from 18K to 145K. The anomaly at ~150K is related to overlapping contributions from the Curie point (shifted downward because of the size effect) and a dielectric relaxation process. The behavior of three relaxation modes observed at temperatures below 145K is discussed, based on the model proposed by Malcherek of polar nanoregions in the orthorhombic phase of Cd2Nb2O7 and the theory of dielectric response of ferroelectric relaxors by Bokov and Ye.