In order to clarify co-doping effects of trivalent rare earth ions to the ionic conduction and the crystal structure in ZrO2, dc- and ac-measurements along with XRD observations have been carried Out to ((Y0.75La0.25)(1-x)Gd-x)(0.18)Zr0.82O2-sigma by changing x from 0 to 1, where the average ionic radius of (Y0.75La0.25)(1-x)Gd-x is constant, i.e., 1.053 angstrom, being independent of x. These specimens contain dual phases, i.e., cubic and monoclinic phases. Dc conductivity in the heating process differs from that in the cooling process. This hysteresis has been discussed in terms of the monoclinic-cubic phase transition on the basis of XRD results at high temperatures. The x-dependencies of the energy values required for the bulk and grain boundary conductions are strongly related to the ionic radii of the trivalent rare earth ions because the states of oxygen vacancies, which are substantially responsible for ionic conductions, depend upon the rare earth ions that capture the vacancies at lower temperatures. Many combinations of oxygen vacancies and rare earth ions lead to the long-ranged hysteresis. (c) 2005 Elsevier B.V. All rights reserved.