Samples of LixNi0.5Mn0.5O2 and Li,Ni1/3Mn1/3Co1/3O2 were prepared as active materials in electrochemical half-cells and were cycled electrochemically to obtain different values of Li concentration, x. Absorption edges of Ni, Mn, Co, and O in these materials of differing x were measured by electron energy loss spectrometry (EELS) in a transmission electron microscope to determine the changes in local electronic structure caused by delithiation. The work was supported by electronic structure calculations with the VASP pseudopotential package, the full-potential linear augmented plane wave code WIEN2K, and atomic multiplet calculations that took account of the electronic effects from local octahedral symmetry. A valence change from Ni2+ to Ni4+ with delithiation would have caused a 3 eV shift in energy of the intense white line at the Ni L-3 edge, but the measured shift was less than 1.2 eV. The intensities of the "white lines" at the Ni L-edges did not change enough to account for a substantial change of Ni valence. No changes were detectable at the Mn and Co L-edges after delithiation either. Both EELS and the computational efforts showed that most of the charge compensation for Li+ takes place at hybridized O 2p states, not at Ni atoms.