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Chem. shift anisotropy (CSA) tensor parameters have been detd. for the protonated carbons of the purine bases in an RNA kissing complex in soln. by extending the model-independent approach [Fushman, D., Cowburn, D. (1998) J. Am. Chem. Soc. 120, 7109-7110]. A strategy for detg. CSA tensor parameters of heteronuclei in isolated X-H two-spin systems (X = 13C or 15N) in mols. undergoing anisotropic rotational diffusion is presented. The original method relies on the fact that the ratio k2=R/R 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 mol. motion, provided rotational diffusion is isotropic. However, if the overall motion is anisotropic k2 depends on the anisotropy D.dblvert./D.perp. of rotational diffusion. In this paper, the field dependence of both k2 and its longitudinal counterpart k1=R/R are detd. For anisotropic rotational diffusion, our calcns. show that the av. kav = 1/2 (k1+k2), of the ratios is largely independent of the anisotropy parameter D.dblvert./D.perp.. The field dependence of the av. ratio kav may thus be utilized to det. CSA tensor parameters by a generalized model-independent approach in the case of mols. with an overall motion described by an axially sym. rotational diffusion tensor. [on SciFinder (R)]