The anelastic spectra of Li6C60Hx and Na6C60Hx have been measured for the first time. The spectra of composite materials obtained by mixing of LiH and NaH with C60 in a solvent still show the structural phase transition around 260 K and preserve the buckyball dynamics of pure fullerenes but do not show the spectral features of the hydrides. This observation suggests that the composite materials are homogeneous samples in which the hydrides are finely dispersed in the fullerene crystal and therefore lose their features. However, after dehydrogenation and after rehydrogenation both the phase transition and the dynamic process are completely suppressed, indicating a deep modification of the lattice structure, possibly due to polymerization. The present study indicates that Li6C60Hx and Na6C60Hx are homogeneous materials and cannot be considered as constituted by bulk C60Hn and Li(Na)Hx, as suggested by a previous study.