Biaxial thermotropic nematic liquid crystals would be of great importance in liquid crystal display technology. Less than a decade ago, such liquid crystals were suggested. The biaxiality of the phases was confirmed using H-2 NMR spectroscopy of deuterated probe molecules. The spectra were collected from a sample rotating around an axis perpendicular to the external magnetic field, resulting in a two-dimensional powder pattern. We have proposed an alternate technique that is based on the second order quadrupole shift detectable in Xe-131 NMR spectra of dissolved xenon. The method has many advantages, such as the NMR spectra are taken from a static sample and the Xe-131 quadrupole coupling tensor is extremely sensitive to the symmetry of the phase. In the present study, we report results obtained on a 600-MHz NMR spectrometer. Together with the data of our earlier study, they confirm that the asymmetry parameter of the Xe-131 quadrupole coupling tensor in the nematic phase of a ferroelectric liquid crystal is 0.85 and in the smectic A phase ca 0.62, indicating significant phase biaxiality. Copyright (c) 2014 John Wiley & Sons, Ltd.