We present the use of ab-initio calculations and the kinetic Monte Carlo method to develop atomic-scale structure-stability relationships for Pt-Ni nanoparticles, promising catalysts for the oxygen reduction reaction (ORR). Although the practical use of Pt-Ni catalysts is limited by Ni dissolution under cell operating conditions, it has recently been shown that it is possible to stabilize octahedral Pt–Ni nanoparticles by alloying them with transition metals (e.g. Mo, Cu, and Rh). We discuss two examples of alloyed Pt-Ni nanoparticles: Mo-Pt-Ni and Cu-Pt-Ni. Using a newly developed kinetic Monte Carlo (KMC) model based on cluster expansions, we demonstrate that Mo atoms are preferentially located on the vertex and edge sites of Mo-Pt-Ni in the form of oxides which are stable within the wide potential window of the electrochemical cycle. These surface Mo oxides help protect Ni in sub-surface layers against acid dissolution. KMC simulations reveal that the enhanced stability of Cu-Pt-Ni is likely due to the reduction of the number of Ni and Cu atoms on the surface during synthesis, reducing the opportunity for Ni and Cu atoms in sub-surface layers to move to the surface and dissolve.