Molecular dynamics of caesium and lead chlorates (hydrated form) has been studied by "Cl nuclear quadrupole resonance (NQR) spectroscopy. The occurrence of only one resonance line for the two compounds in the whole temperature range studied testifies to the crystallographically equivalent positions of their molecules in elementary cells. The relaxation processes in the two chlorates have been found to be analogous to those in the other chlorates not undergoing phase transitions. Analysis of the temperature dependence of the spin-lattice relaxation time has indicated that at low temperatures the dominant relaxation mechanism consists of torsion vibrations (C1O3 anion libration), whereas at 260 K the hindered rotation of the chlorate ion about the threefold axis sets on and its activation energy is 50.0 kJ/mol. The temperature dependence of the resonance frequency for the two chlorates studied is best described by the Brown model extended over the low-temperature range, which indicates large anharmonicity of the vibrations.