Cathode reaction models for solid oxide fuel cells with proton conducting electrolyte (H-SOFC) are proposed, and the reacting orders for each elementary step with respect to oxygen and water vapor partial pressure are Calculated. The limiting steps of cathode reactions are investigated with Sm0.5Sr0.5CoO3-delta (SSC)-BaCe0.8Sm0.2O3-delta (BCS) composite cathodes. The results suggest that the migration of protons to TPBs and the surface diffusion of O-ad(-) might be the limiting reactions for SSC-BCS composite cathodes in wet atmosphere, while the oxygen ions transferring into electrolyte, the reducing of O-ad to O-ad(-), and surad face diffusion of O-ad(-) might be the limiting reactions for SSC-BCS composite cathode in dry atmosphere. (C) 2009 Elsevier B.V. All rights reserved.