Ab initio calculations have been carried out on the potential energy curves of the Rydberg states of NeH up to 3d. Quantum defect functions have been calculated from the ab initio potentials and potential energy curves and vibrational levels for higher n (s,p,d) Rydberg states have been generated. The interaction of the 2p B (2) Pi state with the 2s and 2p, A (2) Sigma(+) and C (2) Sigma(+) states and their predissociation by X C-2(+) has been treated by multi-state complex coordinate scaling calculations for both NeH and NOD. The results are consistent with previous 2X2 calculations on the predissociation of the A (2) Sigma(+) and C (2) Sigma(+) states. Finally, a calculation of the interaction between the (2) Pi, (2) Sigma(+), and (2) Delta 3d states in NeH and NeD shows appreciable mixing between the states at high values of the rotational quantum number.