SrCu3Ti4O12, La2/3Cu3Ti4O12, and Bi2/3Cu3Ti4O12 ceramics were representatively investigated to obtain a systematical understanding about the dielectric behaviors of the compositionally and structurally CaCu3Ti4O12-like oxides and the underlying related mechanism. In opposite to the literature results, giant dielectric-permittivity phenomena with low-frequency epsilon' larger than 1.5 x 104 have been observed in all of these ceramics. Furthermore, the existence of CuO secondary phase has been confirmed in them. In general, the results can be explained by the similar mechanism of internal barrier layer capacitance effect formerly proposed for CaCu3Ti4O12 ceramics and indicate that the giant-epsilon' phenomena should be quite common in the large family of compositionally and structurally CaCu3Ti4O12-like oxide ceramics.