Abstract: Alpha gypsum hemihydrate is obtained by calcining calcium sulfate dihydrate, generated with flue-gas desulfurization of power plants or by chemical process, e.g. in the production of phosphoric acid. The calcining process comprises producing initially a dispersion from calcium sulfate dihydrate and diluted, sulfuric acid solution and heating same at a predetermined rate to about 373 K with industrial, dust-free waste heat, whereupon the solid components are separated from the aqueous sulfuric acid and are dried. An alpha gypsum hemihydrate practically free from anhydrite II is obtained from a solution of sulfuric salts in the diluted sulfuric acid. An addition of magnesium oxide yields a hemihydrate with a high degree of fineness and avoids blooming effects.