To optimize the compositions of new high-strength aluminum ATs7NZh and ATs6N0.5Zh alloys (economically alloyed nikalins), the thermodynamic optimization of the Al-Zn-Mg-Cu-Ni-Fe system is performed via the construction of polythermal sections and the calculation of the chemical composition and volume fraction of phases at characteristic temperatures. The concentrations of the matrix elements (Zn, Mg, Cu) that determine the high level of mechanical properties are shown to be 6–7 wt % Zn, 2–3 wt % Mg, and up to 0.3 wt % Cu. The concentrations of the eutectic-forming elements (Ni, Fe) that ensure the solidification of (Al) + Al9FeNi eutectic are determined. This eutectic favors an increase in the manufacturing properties of the alloys during casting, metal forming, and welding along with a retained high level of the mechanical properties. In general, experimental results confirm the calculated data.