The hydrogen dynamics in the metalhexahydrateperchlorates with Mg, Mn, Fe, Ni, and Zn as metal ions has been investigated with quasielastic neutron scattering. The water molecules perform 180 degrees-flip motions on a picosecond time scale through a series of solid-solid phase transitions. In the highest temperature phase I and the subsequent phase II, rotational barriers of typically E-a = 50 meV are found. These values are surprisingly small in view of the low symmetry of H2O molecules. The I --> II phase transition has only very small effects on the hydrogen dynamics. At the transition into phase III an increase of the rotational barriers to typically E-a = 250 meV is found. This is interpreted as the formation of weak hydrogen bonds. In phase I 180 degrees-flip motions provide a complete description of the observed data. In phases II and III an extension of the dynamical model toward a stronger localization of hydrogen is required. A preference is given to a mechanism leading to a temporary blockade of the flip motions. In phase III of the Fe compound, the existence of crystallographically different sites for water molecules is inferred.