A review is given of the math. foundations of av. Liouvillian theory and examples are provided of av. Liouvillian expressions derived for sequences in NMR which possess temporal symmetry or antisymmetry. The utility of this approach is demonstrated in the design of pulse sequences to measure the effect of cross-correlation between chem. shift anisotropy and dipolar couplings on relaxation rates in biomols. Exptl. verification of the theory is carried out on a 15N labeled sample of ubiquitin. [on SciFinder (R)]