We describe the application of a recently developed two-dimensional nuclear magnetic resonance (2D NMR) technique, variable-angle correlation spectroscopy, to the analysis of molecular motions in complex unlabeled solids. This technique separates the broad anisotropic chemical shift line shapes of nuclei in a sample according to the isotropic shift of each site. It can therefore be used to characterize molecular reorientations by monitoring the changes that these processes introduce in the resolved powder patterns as a function of temperature. Using the C-13 NMR anisotropies of dimethylsulfone as a test case, we explored the potential applications of following such an approach. It was found that in contrast to what happens in nonexchanging systems, the anisotropic line shapes resolved by the variable-angle technique on an exchanging solid are different from line shapes that at similar temperatures can be recorded from a nonrotating sample. An explanation for these differences is presented, and the complete theory required to extract kinetic and geometric information from the experimental 2D line shapes is introduced and illustrated with computer simulations. The capability of this approach to analyze motions in complex systems is further demonstrated with a natural-abundance C-13 variable-temperature NMR analysis of L-tyrosine ethyl ester; a reorienting compound possessing up to 11 inequivalent carbon sites in the solid phase.