The sequence of phase transitions at temperatures from 290 to 420 K in the crystals of Cs5H3(SO4)(4) . 0.5H(2)O (CTSM) and Cs5D3(SO4)(4) . 0.5D(2)O (DCTSM) was studied by Brillouin Light scattering and neutron diffraction. Anomalies in the temperature dependences of the velocity and damping of hypersonic acoustic phonons in the vicinity of 360 K were observed in the CTSM crystal. In contrast, no anomalies were found in the DCTSM crystal. Preliminary analysis of neutron diffraction data does not show symmetry changes in the temperature range studied. Thus it has been found that deuteration of the CTSM crystals leads to a change in the sequence of phase transitions.