The structural properties and relaxation processes of $MCsSO_4$ (M = Na, K, or Rb) crystals were investigated by measuring the NMR spectra and spin-lattice relaxation rates $1/T_1$ of their $^{23}Na$, $^{39}K$, $^{87}Rb$, and $^{133}Cs$ nuclei. According to the NMR spectra, the $MCsSO_4$ crystals contain two crystallographically inequivalent sites each for the M and Cs ions. Further, the relaxation rates of all these nuclei do not change significantly over the investigated temperature range, indicating that no phase transitions occur in these crystals in this range. The variations in the $1/T_1$ values of the $^{23}Na$, $^{39}K$, $^{87}Rb$, and $^{133}Cs$ nuclei in these three crystals with increasing temperature are approximately proportional to $T^2$, indicating that Raman processes may be responsible for the relaxation. Therefore, for nuclear quadrupole relaxation of the $^{23}Na$, $^{39}K$, $^{87}Rb$, and $^{133}Cs$ nuclei, Raman processes with n = 2 are more effective than direct processes.