Muon spin relaxation and powder neutron diffraction have been combined to study three lithium cobalt nitride battery materials. Neutron diffraction shows that these retain the P6/mmm space group of Li(3)N with Co located only on Li(1) sites. The lattice parameters vary smoothly with the degree of metal substitution, such that the [Li(2)N] layers expand while the layer separation contracts, as observed previously for similar series of Cu- and Ni-substituted materials. However, in contrast to the latter, the Li(3-x-y)Co(x)N phases exhibit Curie-Weiss paramagnetism and this prevents the use of nuclear magnetic resonance to measure Li(+) transport parameters. Therefore, muon spin relaxation has been employed here as an alternative technique to obtain quantitative information about Li(+) diffusion. Muon spin relaxation shows that Li(+) diffusion in Li(3-x-y)Co(x)N is anisotropic with transport confined to the [Li(2)N] plane at low temperature and exchange between Li(1) and Li(2) sites dominant at high temperature. By a comparison with previous studies some general trends have been established across a range of Cu-, Ni- and Co-substituted materials. For intra-layer diffusion E(a) decreases as metal substitution increases and the corresponding expansion of the layers results in a more open pathway for Li(+) diffusion. However, an optimal value of x is found with a ≈ 3.69 Å after which the concomitant contraction in layer spacing reduces the polarizability of the lattice framework.