Simple pulse sequences have been used to determine and isolate most carbon-13 and fluorine-19 longitudinal relaxation parameters in pure hexafluorobenzene (carbon-13 in natural abundance). The derived parameters include fluorine-19 and carbon-13 specific relaxation rates (at different field values), dipolar fluorine-carbon cross-relaxation rate, and dipolar (C-13-F-19)-chemical shift anisotropy (C-13 Or F-19) cross-correlation rates. From these experimental parameters, it was possible to estimate the reorientational anisotropy of liquid hexafluorobenzene and to extract the shielding tensor elements of fluorine-19 and carbon-13. Comparison with those elements as determined from solid-state NMR shows a good agreement for fluorine-19 but one important difference (for one element) in the carbon-13 shielding tensor. This feature is confirmed by quantum chemistry calculations and can be explained by the particular ordering in pure solid.