Abstract: Dynamic processes such as chemical exchange or rotations between inequivalent orientations can affect the magic-angle-spinning (MAS) and the multiple-quantum (MQ) MAS NMR spectra of half-integer quadrupolar nuclei. The present paper discusses such dynamic multi-site MAS and MQMAS effects, and applies them to study the dynamic processes that occur in the double perovskite Cryolite, Na3AlF6. Dynamic lineshape simulations invoking a second-order broadening of the central transition and relying on the semi-classical Bloch-McConnell formalism for chemical exchange, were performed for a variety of exchange models possessing different symmetries. Fitting experimental variable-temperature Cryolite 23Na NMR data with this formalism revealed that the two inequivalent sodium sites in this mineral undergo an exchange characterized by a broad distribution of rates. In order to further assess this dynamic process a variety of 27Al and 19F MAS NMR studies were also undertaken; quantitative 27Al-19F dipolar coupling measurements then revealed a dynamic motion of the AlF6 octahedra that were qualitatively consistent with predictions stemming from molecular dynamic simulations on this double perovskite.