Electric conduction in the solid oxide fuel cells electrolyte, La0.5Sr0.5Ga0.6Ti0.4O3-δ, 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, Rb and Rgb, estimated in impedance analyses are nearly in agreement with dc resistance. Though Rb Rgb at T < 650 K, their relative relation is reversed at T>650 K. Since reciprocal resistance is proportional to conductivity, temperature dependencies of T/Rb and T/Rgb yield activation energies for conductions in the bulk and boundary. Two relaxation processes show up in dielectric properties, i.e., low-frequency relaxation peak clue 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, EM, and energies required for creation of a free oxygen vacancy assisting O2- migration, EO. The sums of EM and EO in high- and low-frequency peaks are mostly in agreement with activation energies estimated from temperature dependencies of T/Rb and T/Rgb. [ABSTRACT FROM AUTHOR]