Using charge self-consistent cluster Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) band-structure calculations, the authors have studied the hyperfine fields on both Ni and Fe sites in the NixFe1-x alloys. To elucidate the influence of relativistic effects the hyperfine matrix elements have been calculated nonrelativistically as well as completely relativistically The dependence of the hyperfine fields on the environment of a given site has been studied by performing calculations for various atomic configurations around that site. The results of the work are compared with other theoretical data and with experiment.