The spin-orbit effects were investigated on the complexes involved in the electron self-exchange between Np(V) and Np(VI) in both the outer-sphere and inner-sphere mechanisms, the latter for binuclear complexes containing hydroxide, fluoride, and carbonate as bridging ligands. Results obtained with the variation-perturbation and the multireference single excitation spin-orbit Cl calculations are compared. Both effects due to different relaxations of spinors within a multiplet (spin-orbit relaxation) and scalar (electrostatic) relaxation effects in the excited states are accounted for in the latter scheme. The results show that the scalar (electrostatic) relaxation is well described by the single-excitation spin-orbit CI, and that spin-orbit relaxation effects are small in the Np complexes, as in the lighter d-transition elements but in contrast to the main group elements.