A series of extended reversible phase transitions at similar to 0.1, 1.5, 2.0, and similar to 5 GPa was observed for the first time in the crystals Of DL-cysteine by Raman spectroscopy. These are the first examples of the phase transitions induced by increasing pressure in the racemic crystal of an amino acid. In the crystals of the orthorhombic L-Cysteine, a sequence of reversible structural changes in the pressure range between 1.1 and 3 GPa could be observed by Raman spectroscopy, instead of a single sharp phase transition at 1.9 GPa reported previously in (Moggach, et al. Acta Crystallogr. 2006, B62, 296-309). The role of the movements of the side -CH2SH groups and of the changes in the hydrogen-bonding type in DL- and L-cysteine during the phase transitions with increasing pressure is discussed and compared with that on cooling down to 3 K.