The conductivities of the Zn1-x-yMxMy'O (M, M' = Al, In, Ga, Y) and Zn1-xMxO (M = Al, In, Ga) systems were measured from room temperature to 1173 K in order to elucidate a dominant parameter of the conducting mechanism. The conductivity at 873 K first increased with the dopant content. However, it showed a maximum value at a given dopant content, and then gradually decreased. For the samples with the same dopant content, their conductivity at 873 K was strongly dependent on the mean dopant-ion radii, and reached a maximum value at around 0.51 Angstrom of the mean dopant-ion radii. The results suggested that the conductivity of the system would be influenced not only by the dopant content, but also by the mean dopant-ion radii. It was found that the co-doped ZnO system of Zn0.995Al0.003In0.003O had a conductivity higher than that of the other usual mono-doped system. (C) 2003 Kluwer Academic Publishers.