The magnetic nature of lithium insertion materials of LiNi1-xCoxO2 (x = 0, 1/4, 1/2, 3/4, and 1) were investigated by means of positive muon-spin rotation/relaxation (mu+SR) spectroscopy combined with X-ray diffraction (XRD) analyses and susceptibility measurements. Zero field mu+SR spectra for all the samples below 300 K were well fitted by a dynamic Kubo-Toyabe function, indicating the existence of randomly oriented magnetic moments even at 2 K, i.e., disordered state. The field distribution width Delta due to magnetic Ni3+ ions decreases exponentially with increasing x, suggesting that the Co substitution is likely to simply dilute Ni moments. This also supports that cobalt and nickel ions are homogeneously distributed in a solid matrix even in a muon-scale (microscopically), which is consistent with the results of macroscopic measurements. (C) 2007 Elsevier B.V. All rights reserved.