Chemical shift anisotropy (CSA) tensor parameters have been determined for the protonated carbons of the purine bases in an RNA kissing complex in solution by extending the model-independent approach [Fushman, D., Cowburn, D. (1998) J. Am. Chem. Soc. 120, 7109-7110]. A strategy for determining CSA tensor parameters of heteronuclei in isolated X-H two-spin systems (X = C-13 or N-15) in molecules undergoing anisotropic rotational diffusion is presented. The original method relies on the fact that the ratio kappa(2)=R-2(auto)/R-2(cross) of the transverse auto- and cross-correlated relaxation rates involving the X CSA and the X-H dipolar interaction is independent of parameters related to molecular motion, provided rotational diffusion is isotropic. However, if the overall motion is anisotropic kappa(2) depends on the anisotropy D parallel to/D-perpendicular to of rotational diffusion. In this paper, the field dependence of both kappa(2) and its longitudinal counterpart kappa(1)=R-1(auto)/R-1(cross) are determined. For anisotropic rotational diffusion, our calculations show that the average kappa(av) = 1/2 (kappa(1)+kappa(2)), of the ratios is largely independent of the anisotropy parameter D parallel to/D-perpendicular to. The field dependence of the average ratio kappa(av) may thus be utilized to determine CSA tensor parameters by a generalized model-independent approach in the case of molecules with an overall motion described by an axially symmetric rotational diffusion tensor.