Results are presented of incoherent quasi-elastic neutron-scattering measurements in ethyl 4-(4′acetoxybenzylidene) aminocinnamate (EABAC) in crystal,SAand nematic phases. Discussion is concentrated on data for theSAphase of an aligned, tail deuteriated, sample forQ⊥nandQ‖n, whereQis the scattering vector andnthe direction of the unique axis (the layer normal). The scattering lawS(Q, ω) 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 withDr∼3×1010rad 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 ∼ 10-11s.