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We report first-principles calculations for determining the phase relationships in multi-component cathode materials. We investigate the effect of delithiation on the phase stability, chemical potential, and open circuit voltage for a selection of cathode materials based on Li–Mn–Ni oxides at various temperatures. Entropic contributions are included by calculating the phonon frequencies in the harmonic approximation. The open circuit voltage in multi-component systems is estimated by a convex hull approach. We confirm that spinel-like phases are predominant during the charging process of layered Li–Mn–O cathode materials and that the addition of Ni reduces the spinel content. The analysis of phase stability upon delithiation suggests that the Li2MnO3 component in the Li2MnO3·Li(Mn,Ni)O2 electrode material should not exceed 60% and that the amount of Ni in the LiMnO2 component should be above 40 at% for minimizing spinel-type phase formation and minimizing oxygen formation. Using the computed structural stability at room temperature, we derive property maps for the design of Li–Mn–Ni–O cathode materials.