Electric conduction in the solid oxide fuel cells electrolyte, La0.5Sr0.5Ga0.6Ti0.4O3-delta, has been elucidated by dc and ac measurements as a function of temperature from 528 to 1103 K. The sum of resistances in the bulk and boundary, R-b and R-gb, estimated in impedance analyses are nearly in agreement with dc resistance. Though R-b<R-gb at T<650 K, their relative relation is reversed at T>650 K. Since reciprocal resistance is proportional to conductivity, temperature dependencies of T/R-b and T/R-gb yield activation energies for conductions in the bulk and boundary. Two relaxation processes show up in dielectric properties, i.e., low-frequency relaxation peak due to conduction in the boundary and high-frequency peak resulting from bulk conduction. Temperature dependencies of resonance frequencies and maxima of dielectric parameters in these relaxation peaks are used to estimate migration energies of O2- ion, E-M, and energies required for creation of a free oxygen vacancy assisting O2- migration, E-O. The sums of E-M and E-O in high- and low-frequency peaks are mostly in agreement with activation energies estimated from temperature dependencies of T/R-b and T/R-gb. (C) 2004 American Institute of Physics.