EPR of low-spin Ni3+ ions is used to refine Ni3+-Ni2+ segregation in LixNi2-xO2 oxides with 0.6 less-than-or-equal-to x < 1 where a transformation from cubic to layered structure occurs. It is shown that, above the temperature of magnetic ordering, the spin-lattice relaxation comprising phonon modulation of antiferromagnetic interplane Ni3+-O-Ni2+ and ferromagnetic intraplane Ni3+-O-Ni3+ interactions governs the linear temperature dependence of the EPR line width (DELTAH(pp)). The dDELTAH(pp)/dT coefficient can be used as a parametersensitive to the Ni2+-Ni3+ segregation in neighbouring cubic (111) planes. For LixNi2-xO2 (0.6 < x < 0.7), where Li+, Ni3+ and Ni2+ are approximately in the same amounts, clustering of the Li+, Ni3+ and Ni2+ ions takes place in the alternative (111) planes. For x > 0.7, Li+ and Ni3+ segregation evolve two discrete LiO2- and NiO2-layers, but a small part of Li+ and Ni3+ fall into the "alien" layer. In addition, Ni2+ segregate into both layers, their amount being almost equal when x > 0.7.