Resolved laser induced fluorescence spectra of ⁵⁸NiD, recorded at Doppler resolution between 11000 and 18000 cm^-1 have established more than 200 term energies in two of the three strongly interacting, low-lying states (²Δ, ²Π, ²Σ⁺) of NiD, associated with an Ni⁺(3d⁹)D^- configuration. Our observations span v= 0-5 in the lowest spin-orbit component of the ground state, X ²Δ_5/2, v = 0-3 in X ²Δ_3/2 and v = 0-1 in the lower component of the W ²Π_3/2 state. Collisional processes populate several neighbouring excited states, allowing us also to locate the first rotational levels of A(Ω = 5/2) v = 1, I(Ω = 3/2) v = 0 and E(Ω = 3/2) v = 1 at 16664.8, 17367.3 and 17508.1 cm^-1 respectively. Spin-orbit and rotation-electronic interactions are strong in NiD (as in NiH), and with no direct observation of either of the Ω" =1/2 states, meaningful representations of the low-lying energy levels is difficult. We have therefore attempted a global, multi-isotope fit to reproduce the term energies of the known term energies of NiD and ^58,60,62NiH (where some Ω" =1/2 levels are known). Dunham-type parameters have been used to represent the unperturbed ²Δ, ²Π and ²Σ⁺ states, with off-diagonal matrix elements (treating spin-orbit, L- and S-uncoupling effects) based on Ni⁺ atomic properties. Born-Oppenheimer breakdown terms were included in the model. The equilibrium bond lengths for ⁵⁸NiH/⁵⁸NiD are 1.4545(1)/1.4559(1) Å for the X ²Δ state and 1.5094(2)/1.5083(2) Å for the W ²Π state.