Numerous molecules are asymmetric in shape and diffuse anisotropically in solution. Moreover, many local motions contribute to the nuclear magnetic relaxation process. Dipole-dipole cross-correlations depend on both geometrical (i.e., the average orientations of the Bipolar vectors with respect to the principal axes of the diffusion tensor) and dynamical parameters (i.e., the local motions of the same: dipolar vectors). We derived a new expression of the cross-correlation function that takes anisotropy of diffusion and local motions of small amplitude into account. The local motion of a unit dipolar vector is expressed in terms of the projection of the vector onto the plane that is perpendicular to its average position. Cross-correlations have been used to study the influence of dynamics on the determination of the angle between the two dipolar vectors.