Investigations of Li diffusion in stage-1 and stage-2 Li graphite intercalation compounds with neutron time-of-flight and backscattering techniques and β-radiation detected nuclear magnetic resonance/relaxation (β-NMR) with the nucleus 8Li(T1/2 = 0.8 s) are reviewed and compared. Depending on temperature, the spin-lattice relaxation-rate T1 -1of 8Li is governed by different processes. Above 300 K, T1 -1(T) shows maxima induced by long-range Li+diffusion. Jump correlation times are estimated. Inspection of the B field dependence of T1 -1revealed two-dimensional diffusion behaviour. The neutron spectra showed a quasielastic line broadening above 500 K, which was used to obtain diffusion coefficients and to trace jump vectors of the in-plane motion. The diffusion parameters observed with both techniques are compared, and differences that show up are discussed. In addition, the low-temperature spin-lattice relaxation rates, being due to coupling to conduction electrons, are used to explore electronic properties.