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The exceptional mechanical properties of Ni-based high entropy alloys are due to the presence of ordered L12 (γ′) precipitates embedded within a disordered matrix phase. While the strengthening contribution of the γ′ phase is generally accepted, there is no consensus on the precise contribution of the individual strengthening mechanisms to the overall strength. In addition, changes in alloy composition influence several different mechanisms, making the assessment of alloying conditions complex. Multicomponent L12-ordered single-phase alloys were systematically developed with the aid of CALPHAD thermodynamic calculations. The alloying elements Co, Cr, Ti, and Nb were chosen to complexify the Ni3Al structure. The existence of the γ′ single phase was validated by microstructure characterization and phase identification. A high-temperature compression test from 500 °C to 1000 °C revealed a positive temperature dependence of strength before reaching the peak strength in the studied alloys NiCoCrAl, NiCoCrAlTi, and NiCoCrAlNb. Ti and Nb alloying addition significantly enhanced the high-temperature yield strengths before the peak temperature. The yield strength was modeled by summing the individual effects of solid solution strengthening, grain boundary strengthening, order strengthening, and cross-slip-induced strengthening. Cross-slip-induced strengthening was shown to be the key contributor to the high-temperature strength enhancement. [ABSTRACT FROM AUTHOR]