The electrical conductivity of σ-phase Pr 1- yGd yO 1.5+ δ ( y = 0.0, 0.1, 0.2, and 0.4) was measured as a function of temperature and oxygen partial pressure. The dependence of the electrical conductivity of Pr 1- yGd yO 1.5+δ on the composition was determined by combining gravimetric and conductivity data. The results are consistent with the small-polaron model of localized charge carriers hopping between two adjacent Pr ions in different valence states. The following equation was quantitatively examined: σ = ns(1- s) pekh, where n is the concentration of total Pr ions, s is the fraction of Pr 4+ ions in total Pr ions, p is the probability that cationic positions are occupied by mixed valence ions, and kh is a constant characteristic of the charge-transfer process between different valence states. It was found that kh increases slightly with increasing δ. This dependence is discussed in terms of the observed activation energy and the degree of delocalization of the 4 f electrons.