Ni ₃X-type intermetallic compounds, also often referred to as γ′, γ ^″, and η precipitates in Ni-base alloys, have been investigated by first-principles methods. Thermodynamic and mechanical stability of Ni ₃X (X = Al, Ti, Nb, Mo, Fe, and Cr) compounds has been determined by density functional theory calculations of formation enthalpies and elastic properties of their L1 ₂, D0 ₂₂ and D0 ₂₄ phases. In addition, we have investigated the site preference behavior of Al, Ti, Nb, Mo, Fe, and Cr solutes in the L1 ₂-structure Ni ₃Al, Ni ₃Ti, and Ni ₃Nb intermetallic compounds and used this information to investigate the solubility of the aforementioned alloying elements. Our results show that the most stable structures of Ni ₃Al, Ni ₃Ti, Ni ₃Nb, Ni ₃Cr, Ni ₃Mo, and Ni ₃Fe at 0 K are L1 ₂, D0 ₂₄,D0 ₂₂, D0 ₂₄, D0 ₂₂, and L1 ₂ respectively.