A ligand-field theory has been developed for transition-metal diatomics having electronic configurations of d9(A)d(B)10sigma2, d9(A)d9(B)sigma2, and d(A)8(3F)d(B)10sigma2sigma*1. The theory treats each atom as a point charge and includes spin-orbit interactions. No contributions due to d-orbital chemical bonding are included. Since the d orbitals are quite small compared to the bond lengths in these molecules, the only inputs to the theory are the ligand charges (Z(A) and Z(B)), the radial expectation values [r(A)2]nd, [r(B)2]nd, [r(A)4]nd, and [r(B)4]nd, the atomic spin-orbit parameters zeta(A) and zeta(B), and the bond length, R. Calculations employing no adjustable parameters (setting Z(A,B) = +1.0, and using radial expectation values and spin-orbit parameters from atomic tables) provide essentially quantitative agreement with ab initio results on the d(Ni)9d(Cu)10sigma2 manifold of states in NiCu, and on the d(A)9d(B)9sigma2 manifold of states in Ni2. This demonstrates that the ligand-field model has some validity for metal molecules containing nickel, primarily because of the compact nature of the 3d orbitals in this element. Similar calculations of the d(A)9d(B)9sigma2 manifold of states in Pt2 and the d(Ni)9d(Pt)9sigma2 manifold of states in NiPt are presented for comparison to future ab initio or experimental measurements, although the possibility of d-orbital contributions to the bonding in these species makes the ligand-field model less favorable in these examples. The d(Ni)8(3F)d(Cu)10sigma2sigma*1 excited electronic states of NiCu, which are well known from resonant two-photon ionization spectroscopy, are also investigated in the ligand-field model. As a final example, the d(Ni)8(3F)sigma2sigma*1 excited electronic states of NiH are also examined using the same treatment as that employed for the d(Ni)8(3F)d(Cu)10sigma2sigma*1 excited manifold of NiCu.