Process with calcium sulfite hemihydrate in a powdery byproduct from dry flue gas desulfurization for the production of fly ash cement

In a process of production of fly ash cement by grinding portland cement clinker containing CaO.multidot.Al.sub.2 O.sub.3 with fly ash and gypsum as solidification regulator, the improvement of using in place of fly ash and gypsum a powdery byproduct, which is recovered in anhydrous flue gas desulfurization process, said flue gas resulting from the combustion of fossil fuel and carrying along at least a part of the fly ash which also results during said combustion, said flue gas being treated in an absorber with a calcium-containing suspension (absorbing substance) in such a way that solid material leaves said absorber as dry end product which is at least partially added to at least one dust removing apparatus and is filtered off, said byproduct having a composition of 20 to 95% by weight fly ash, and 5 to 80% by weight of calcium-containing reaction products of the desulfurization process in which byproduct SO.sub.2.sup.- exceeds SO.sub.3.sup.- and the essential reaction product which functions as solidification regulator is calcium sulfite hemihydrate.