This paper presents a study of mathematical modeling and steady-state analysis of a proton-conducting solid oxide fuel cell (SOFC). The SOFC has a SrCe0.95Yb0.05O3-alpha (SCY) electrolyte and two platinum electrodes. A mathematical model of the SOFC is first developed. The model captures electrochemical processes as well as the transport phenomena. The existence of steady-state multiplicity in the cell under three modes of constant ohmic load, potentiostatic and galvanostatic operations is studied. Simulation results show that a multiple steady-states region exists at low inlet fuel and air temperatures under constant ohmic load and potentiostatic operations. The occurrence of ignition and extinction in the cell solid (electrolyte, anode and cathode) temperature is reported. This result is in agreement with those for oxygen ion-conducting solid oxide fuel cells in which the existence of steady-state multiplicity has been attributed to the dependence of the electrolyte oxygen-ion conductivity on temperature. This work shows that concentration and temperature multiplicities coexist. (C) 2012 Elsevier Ltd. All rights reserved.