Results are presented of incoherent quasi-elastic neutron-scattering measurements in ethyl 4-(4’acetoxybenzylidene)aminocinnamate (EABAC) in crystal, Sa and nematic phases. Discussion is concentrated on data for the Sa phase of an aligned, tail deuteriated, sample for Q ┴n and Qn, where Q is the scattering vector and n the direction of the unique axis (the layer normal). The scattering law S(Qw) is found to be essentially identical for the two directions. Analysis of the results shows that the molecules undergo rapid reorientation about the long axes with Dr˜ 3 x 1010 rad s-1, together with a random but bound motion predominantly normal to the layers with an r.m.s. amplitude <Z2>1/2˜ 1.2-1-8 Å, depending on the model, and a correlation time ˜ 10-11 s.