A mathematical model of a solid oxide fuel cell (SOFC) with a BaCe 1xSmxO3α type electrolyte is developed. This class of electrolytes exhibits both proton and oxygen-anion conductivity. To develop the model, heat transfer, mass transfer and electrochemical processes are taken into account. The existence of steady-state multiplicity in this class of fuel cells is investigated under three operation modes: constant ohmic load, potentiostatic and galavanostatic. The cell has up to three steady states under the constant ohmic load and potentiostatic modes, and a unique steady state under the galvanostatic mode. This same steady state behavior has been observed in oxygen-anion conducting and proton conducting SOFCs. Interestingly, this study shows that in this class of SOFCs, thermal and concentration multiplicities can coexist; ignition in the solid temperature is accompanied by extinction in the fuel and oxygen concentrations, and ignition and extinction in concentrations of water in the anode and cathode sides, respectively.