Two perovskite-type compounds, (MA)(2)[B'Co(CN)(6)] (MA = methylammonium, B' = K(I) and Na(I)), have very similar structures, but exhibit marked differences in the phase and dielectric transitions. Solid state H-2 NMR studies reveal the detailed dynamic changes of the caged methylammonium (MA) cations before and after the phase transitions, which are correlated with the different dielectric states of the compounds. Using solid state Co-59 NMR, the dynamic changes of the host lattices before and after the transitions, which accompany the changes in the dynamics of the caged MA cations, are unveiled, demonstrating the intriguing interplay between the MA cations and the host lattices. On the basis of these observations, the molecular origins of the dielectric transitions are discussed in detail.