Translational self-diffusion measurements have been performed in the mesophases of the p-hexyloxybenzylidene-p -fluoroaniline (FAB.OC6) liquid crystal, by means of a static fringe field gradient approach. The method provides an accurate enough data set of the diffusion tensor as a function of temperature in the nematic and smectic A phase to be used for accurate analysis exploiting well established self-diffusion models. Also measurements in the smectic B phase have been carried out and the results obtained seem to be consistent with a picture where the out of plane diffusion is strongly inhibited (< 10(-15)m(2)/s) and only a slow in plane diffusion (similar to 10(-13)M(2)/S) is present.