Muon spin relaxation measurements are reported on three members of the Li x MPO 4 series. The magnetic properties of stoichiometric samples with M = Ni, Co, Fe, were investigated at low-temperature. In LiNiPO 4 we observe different forms of the muon decay asymmetry in the commensurate and incommensurate antiferromagnetic phases, accompanied by a change in the temperature dependence of the muon oscillation frequency. In LiCoPO 4 the form of the muon decay asymmetry indicates that the correlation between layers decreases as the Néel temperature is approached from below. LiFePO 4 shows more conventional behaviour, typical for an antiferromagnet. Measurements on Li x FePO 4 with x = 0.8, 0.9 & 1 show evidence for lithium diffusion below ∼ 250 K and muon diffusion dominating the form of the relaxation at higher temperature. The thermally activated form of the observed hopping rate suggests an activation barrier for lithium diffusion of ∼ 100 meV and a diffusion constant of D Li ∼ 10 −10 − 10 −9 cm 2 s −1 at room temperature.