Oxygen concentration cells have often been employed to determine the ionic transference number of a ternary or higher oxide, e.g., LiNbO3 and Ca1-xLi2xWO4, on the basis of Wagner's classic theory [Z. Phys. Chem. B21 (1933) 25]. In this paper, we report on a unusual behavior of EMF of the oxygen concentration cell Pt,a(O2)(1) \LiNbO3\ a(O2)(11) (=0.21),Pt to demonstrate that because of the unspecified, surplus degree(s) of freedom of the oxide, the EW of the cell has no unique meaning in general. The unusual behavior is attributed to cationic unmixing induced by the oxygen potential gradient applied. Special cases are discussed in which one can determine the ionic transference number of ternary or higher oxides from the EMF of an oxygen concentration cell.