Deuteron nuclear magnetic resonance (NMR) and dielectric spectroscopy are utilized to investigate the dynamics in sulfuric acid hydrates as well as in nitric acid hydrates for various degrees of hydration. Near the glass transition temperature the electrical response is up to four decades faster than the calorimetric one, a feature found also for several other inorganic ionic liquids. The acid hydrates display pronounced super-Arrhenius behavior with fragility indices of the order of 100. The relaxation strength of the acid hydrates increases with increasing temperature, an observation that was rationalized with reference to the degree of molecular dissociation. Spin relaxometry and stimulated-echo spectroscopy revealed an overall isotropic reorientation process featuring a jump angle of about 30°. Finally, the implications of the present results for the understanding of the glass transition of pure ultraviscous water are discussed.