Crystallographic and magnetic measurements of the system Li+xNi++1−2xNi+++xO for the entire range 0≤x<0.5 are reported. For values ofx≤0.3, the lattice appears to be antiferromagnetic and is cubic above the Curie temperature. For the range of compositions 0.3<x<0.5, the lattice is rhombohedral and apparently ferrimagnetic, a maximum magnetic moment per gram of 31 cgs cm3/g being observed atx=0.46. A maximum ferrimagnetic Curie temperature of 241°K was observed for the compositionx=0.41. These properties are interpreted in terms of a partial ordering of Li and Ni ions into alternate sets of (111) planes which couple antiparallel to one another, the moments within any set being either ferromagnetically coupled or paramagnetic, depending upon the number of nonmagnetic near neighbors in the neighboring planes.