The electrical conductivities of SrZr0.9Y0.1O3-delta (SZY10) and BaCe0.95Y0.05O3-delta(BCY5) were measured as a function of hydrogen partial pressure P(H-2), oxygen partial pressure P(O-2), steam partial pressure P(H2O) and temperature. Their relaxation processes were analyzed using the solution of Fick's diffusion equation to determine the chemical diffusion coefficients and surface reaction rate constants. There were the differences in chemical relaxation kinetics and the conductivity dependence on P(H2O) between the both oxides. The chemical diffusion coefficients depend on temperature but are essentially independent of P(H-2), P(O-2) and P(H2O). The ambipolar diffusion treatment can explain the temperature dependence of chemical diffusion coefficients quantitatively. The chemical diffusion coefficients of SZY10 is one or two order of magnitude smaller than those of BCY5 at low temperature. The sluggish conductivity relaxation in SZY10 was due to considerably small oxygen vacancy diffusion coefficients at low temperatures. The total conductivity depends on P(H2O) in the case of SZY10, but not for BCY5. This different dependence on P(H2O) is caused by the difference in the ratio between proton mobility and oxide-ion mobility. (C) 2010 Elsevier B.V. All rights reserved.