High-frequency electron paramagnetic resonance (HF-EPR) spectroscopy was employed to examine the oxidation state and local structure of Ni and Mn ions in Ni,Mn-codoped LiCoO2. The assignment of EPR signals was based on Mg,Mn-codoped LiCoO2 and Ni-doped LiCoO2 used as Mn4+ and low-spin Ni3+ EPR references. Complementary information on the oxidation state of transition-metal ions was obtained by solid-state Li-6.7 NMR spectroscopy. For slightly doped oxides (LiCo1-xNixMnxO2 with x < 0.05), nickel and manganese substitute for cobalt in the CoO2 layers and are stabilized as Ni3+ and Mn4+ ions. The local structure of Mn4+ ions was determined by modeling of the axial zero-field-splitting parameter in the framework of the Newman superposition model. It has been found that the local trigonal distortion around Mn4+ is smaller in comparison with that of the host site. To achieve a local compensation of Mn4+ charge, several defect models are discussed. With an increase in the total dopant content (LiCo1-xNixMnxO2 and 0.05 <= x <= 0.10), a saturation in the Ni3+ amount (up to x < 0.05) is attained, while the Mn4+ content increases gradually. Ni3+ ions are surrounded by Co3+ ions only in the whole concentration range (0 < x <= 0.10). The first metal coordination sphere of Mn4+ ions undergoes a transformation with an increase in the total Ni and Mn contents due to a progressive replacement of Co3+ by Mn4+ and Ni2+ ions. For highly doped oxides (LiCo1-xNixMnxO2 with x = 0.10), nickel and manganese achieve, with respect to the local charge compensation, their usual oxidation states of 2+ and 4+.