Spin-polarized self-consistent linear-muffin-tin-orbital band-structure calculations have been carried out at several lattice constants for the set of 15 ordered fcc compounds defined by the formula MnmFenNi4-m-n, where m and n are integers, and 0<=m, n4. Atomic moments for Mn2FeNi, MnFe2Ni, and MnFeNi2 are among those reported here. These results represent the first systematic description of the dependence of the atomic moments on composition and lattice constant over the entire composition range for this system. In addition to providing some insight into the nature of the spin arrangements in these compounds, the calculated moments provide the starting point of a statistical theory of Mn-Fe-Ni alloys that is developed in the following paper. Finally, the magnetic moments of isolated Mn, Fe, and Ni impurity atoms in several Mn-Fe-Ni materials are obtained by extrapolation. © 1990 The American Physical Society.