The alpha and beta forms of 'hemihydrate' and anhydrite III were subjected to X-ray examination at various H//2O partial pressures. Two hydrate stages of 'hemihydrate' are capable of existence. For P(H//2O)/P//O equals 0. 35 and T equals 22 degree C alpha hydrate having the 'idealized' composition CaSO//4 multiplied by (times) 3/6 H//2O is in equilibrium with the environment. This phase is characterized by a monoclinic overstructure cell of space group 12 characterized by alpha //o equals 12. 0275 plus or minus 0. 0004 A, b//o equals 6. 9312 plus or minus 0. 0003 A, c//o equals 12. 6919 plus or minus 0. 0005 A, beta equals 90. 18 plus or minus 0. 01 degree . There are no differences in terms of crystal structure between the alpha and beta forms of hemihydrate and anhydrite III.