During the last 10 years, a lot of interests have been devoted to the so-called CDC (colossal dielectric constant) materials. The first materials exhibiting this behavior were the perovskite-based ceramics on the CCTO (CaCu3Ti4O12) composition. Relative dielectric permittivity can attain values up to (or even larger than) 105. Nevertheless, their dielectric losses are too high, the lower values ranging 10%, in a narrow frequency range, thus limiting their applications. The underlying physical mechanisms at the origin of the CDC are still under study. The analysis of broadband impedance spectroscopy measurements leads most of the authors to propose an interfacial polarization mechanism (at the electrodes or at internal barriers), there is a limited number of complementary electrical characterization techniques, which, up to now, comfort the proposed interfacial polarization mechanisms. In the present work, I-V and time-domain polarization are used to characterize these materials. One of the main results is the observation of a non-symmetrical response of these materials related to the direction of the polarization. These results are observed for both macroscopic level on bulk polycrystalline material and within individual grains of the same samples. These results do not fit current accepted models for polarization for CDC materials.