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The oxygen electrode in a proton-conductor based solid oxide cells is often a triple-conducting material that enables the transport and exchange of electrons (e-), oxygen ions (O2-), and protons (H+), thus expanding active areas to enhance the oxygen electrode activity. In this work, a theoretical model was developed to understand stability of tri-conducting oxygen electrode by studying chemical potentials of neutral species (i.e., μ_(O_2)^ , μ_(H_2)^ , and μ_(H_2 O)^ ) as functions of transport properties, operating parameters, and cell geometry. Our theoretical understanding shows that: (1) In a conventional oxygen-ion based solid oxide cell, a high μ_(O_2)^ (thus high oxygen partial pressure) exists in the oxygen electrode during the electrolysis mode, which may lead to the formation of cracks at the electrode/electrolyte interface. While in a proton-conductor based solid oxide cell, the μ_(O_2)^ is reduced significantly, suppressing the crack formation, and resulting in improved performance stability. (2) In a typical proton-conductor based solid oxide electrolyzer, the dependence of μ_(O_2)^ on the Faradaic efficiency is negligible. Hence, approaches to block the electronic current can improve the electrolysis efficiency while achieving stability. (3) The difference of the μ_(O_2)^ (thus p_(O_2)^ ) between the oxygen electrode and gas phase can be reduced by using higher ionic conducting components and improving electrode kinetics, which lead to further improvement of electrode stability.