The 1H and 133Cs spin-lattice and spin-spin relaxation times of CsH3(SO4)2 and Cs3H(SO4)2 single crystals were measured using nuclear magnetic resonance (NMR) near the phase transition temperatures of these crystals. CsH3(SO4)2 crystals undergo three phase transitions at high temperatures (TC1=320 K, TC2=420 K, and TC3=496 K), whereas Cs3H(SO4)2 undergoes four phase transitions (TC1=225 K, TC2=253 K, TC3=306 K, and TC4=419 K). The behavior of T1 for the 1H and 133Cs nuclei in the two crystals differs markedly. For CsH3(SO4)2, the 1H spin-lattice relaxation time increases with increasing temperature, whereas for Cs3H(SO4)2 this relaxation time decreases with increasing temperature. These results indicate that the molecular motion of 1H in the proton-ric- h CsH3(SO4)2 crystals differs from that of 1H in Cs3H(SO4)2 crystals. The changes in the 1H and 133Cs spin-lattice relaxation times at the phase transition temperatures result from changes in the environments of the 1H and 133Cs nuclei during the transitions. In addition, the spin-lattice relaxation times of the CsH3(SO4)2 and Cs3H(SO4)2 crystals indicate that they have superionic character above TC2 (=420 K) and TC1 (=225 K), respectively. Further, new hydrogen sulfates of alkaline metals are discussed in terms of their hydrogen-bonding systems. For compounds of formula CsXHNSO4 (where M is an alkali metal, X+N=2), the value of N gives the average number of hydrogen donor functions (OH groups) per SO4 tetrahedron. The N value defines the main features of the hydrogen-bonding systems.