The layered AMO(2) compounds (A = alkali metal, M = trivalent octahedral site cations) derived from the simple rock-salt structure have always been considered to have only one crystallographic site for the A and the M atoms. These structures are described in terms of close-packed oxygen layers with interstitial A and M atoms, especially when A = Li. This gives a layer sequence (AO)(-) and (MO)(+). The AMO(2) compounds are part of the compounds in the A-M-O systems such as A(2)MO(3) and A(5)MO(6), which are derived from the rock-salt structure with alternating layers of pure (AO)(-) and mixed [(A,M)O](+) layers with multiple interstitial octahedral sites in the (A,M)O layer for occupation by the different A and M cations. Evidence is presented from Co-59 NMR experiments on LiCoO2 for the existence of at least two sites in the (CoO)(+) layer. Several NMR methodologies, such as the use of various pulse sequence, nutation experiments, and magic angle sample spinning (MASS) are employed. Magic-angle-sample-spinning experiments show only one isotropic peak. However, an analysis of spinning sidebands envelope at various spinning speeds clearly shows the presence of at least two sites. One of these has orthorhombic symmetry and another has axial symmetry, with closely related chemical shift anisotropy components that result in the observation of nearly identical isotropic chemical shifts. The possible importance of the absence or presence of holes on oxygen has been discussed in accounting for the two sites.