Upon Li intercalation in anatase TiO2 spontaneous phase separation in a Li0.01TiO2 Li-poor and a Li0.55TiO2 Li-rich phase occurs with sub-micron domain sizes. When applied as an anode, such two-phase behaviour leads to a constant electrochemical potential during (dis-)charge, provided there is thermodynamic equilibrium between the phases. Using high field solid state nuclear magnetic resonance (NMR), we were able to observe how diffusion of Li between the two phases on millisecond time scales and 100-nm length scales takes care of establishing such an equilibrium. At room temperature similar to10(20) m(-2) s(-1) Li-ions continuously cross the phase boundaries. On much faster microsecond time scales, diffusion takes place within each of the separate phases. Using state of the art neutron diffraction, the Li-ions were found to be located in the Li-poor and Li-rich phases of anatase, which is quite comparable to finding a needle in a haystack. It appears that, due to the distortion of the oxygen octahedra and the small Li-ion size, there are two possible positions in each octahedron. On short picosecond time scales, the Li is hopping between these two sites inside one octahedron (quasi-elastic neutron scattering results and molecular dynamics simulations). (C) 2004 Elsevier B.V. All rights reserved.