In this article we study the lateral molecular diffusion in homogeneous lipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayers by molecular dynamics simulations with the all-atom Optimised Potentials for Liquid Simulations and the coarse-grained MARTINI force field. On the statistically relevant time scales, the centre-of-mass mean-square displacement exhibits in both cases the subdiffusive asymptotic form W (t) 2Dαtα , with α ≈ 0.67 and α ≈ 0.57, respectively. The diffusive dynamics obtained by the MARTINI force field is, however, faster by a factor of about 3. The subdiffusive characteristics of the diffusion process is confirmed by comparing the integral of the centre-of-mass velocity autocorrelation function with its analytical long-time tail. The agreement is particularly good for the MARTINI force field, which permits to extend the simulation length and the system size considerably. Our results are in agreement with experimental observations of subdiffusion in lipid bilayers on longer time scales and do not support the finding of some authors that the latter should be considered as a transient phenomenon.