Microscopic magnetism of the electrochemically Li-deintercaleted LixCoO2 powders has been investigated by muon-spin rotation and relaxation (mu+SR) spectroscopy in the temperature (T) range between 10 and 300 K. Weak transverse-field mu+SR measurements indicate that localized moments appear in LiCoO2 below 60 K, while both Li0.53CoO2 and Li0.04CoO2 are paramagnetic even at 10 K. Zero-field mu+SR measurements for the samples with x = 0.53 and 0.04 show that the field distribution width (Delta) due to randomly oriented nuclear magnetic moments of Li-7 and Co-59 decreases monotonically with increasing T up to 250 K, and then it decreases steeper (increasing slope (d Delta/dT)) above 250 K. Because the muon hopping rate (nu) is almost T independent for Li0.53CoO2 below 300 K, the decrease in Delta suggests that the time scale of Li+ diffusion in LiCoO2 is within a microsecond scale. (C) 2007 Elsevier B.V. All rights reserved.