NMR relaxation parameters were measured for the peptide-plane carbonyl and nitrogen nuclei for the protein Escherichia coil flavodoxin. A poor correlation between the general order parameters of the C'-C alpha vector (Zeng, L.; Fischer, M. W. F.; Zuiderweg, E. R. P. J. Biomol. NMR 1996, 7, 157-162) and the N-NH vector was observed. We interpret this lack of correlation in this nearly spherical protein as evidence of local or semilocal anisotropic motion. A new experiment is introduced from which the cross-correlation between the carbonyl chemical shift anisotropy relaxation and carbonyl-C alpha dipole-dipole relaxation is obtained. We show theoretically that the three relaxation measurements, reporting on the dynamics of the C'-C alpha vector, N-NH vector, and CSA tensor components behave differently under anisotropic motion. The cross-correlation order parameter formalism for dipolar cross-correlation spectral densities, as introduced by Daragan and Mayo (Daragan, V. A.; Mayo, K. H. J. Magn. Reson. B 1995, 107, 274-278), has been extended to include cross-correlations between nonaxial chemical shift anisotropy and dipole-dipole relaxation. By analyzing our experimental data with the theoretical models for anisotropic local motion, dynamic models were obtained for the peptide planes of 32 residues of E. coli flavodoxin.