Second moments (M-2) and spin-lattice relaxation times (T-1) of proton nuclear magnetic resonance (NMR) measurements were analyzed for the hydrogensulfides of sodium, potassium, and rubidium. Three modifications are known at ambient pressure for each of MHS with M=Na, K,Rb. They are isotypic for the different cations, with an ordered monoclinic low temperature modification, a dynamically disordered rhombohedral middle temperature modification (MTM), and a cubic high temperature modification (HTM). The number of proton sites for one proton increases from two in the MTM to at least eight in the HTM. The title compounds were investigated by proton NMR in the temperature range 180 Kless than or equal toTless than or equal to560 K with a resonance frequency of nu(0)=400 MHz. In addition, KHS was measured from T=90 K up to T=297 K, using proton resonance frequencies nu(0)=45 MHz and nu(0)=96 MHz. The M-2 calculated from the absorption signal of the individual modification for the various cations do not differ from those calculated for the known crystal structures. The minima of T-1 are in good agreement with results of calculations based on the crystal structure of the MTM of these compounds and two-site 180degrees reorientations of the anions. Activation enthalpies and attempt frequencies (NaHS:26.2(4) kJ mol(-1), 6.1(2)x10(14) s(-1), KHS:19.0(4) kJ mol(-1), 4.0(7)x10(13) s(-1), RbHS:16.3(4) kJ mol(-1), 2.0(2)x10(13) s(-1)) agree with those determined by quasielastic neutron scattering [Haarmann , J. Chem. Phys. 113, 8161 (2000)]. For the cubic HTM, translational motion of the cations is probable. Only in the case of KHS and RbHS, was the onset of this translational motion already observed in the MTM at temperatures close to the phase transition into the HTM. This seems to be a difference in the mechanism of the MTM--> <--HTM phase transition for NaHS, on the one hand, and KHS, RbHS, on the other hand.