The crystal structures of the three nonstoichiometric compounds Zn 1.685In 2.21S 5, Zn 4.37In 2.42S 8 and Zn 6.13In 2.58S 10 have been determined. Their hexagonal unit cells are of the Wurtzite type with a = 3.85Å, the c-dimensions and space groups being 30.85 Å, P6 3mc; 24.96 Å, P3 m1; 31.30 Å, P3 m1, respectively. All atoms occupy positions on the triad rotation axes. The layer structures show the same principle as all the other known structures in the ZnInS system ( 1-5). They are based on slightly distorted close packing of the sulfur atoms with Zn in tetrahedral voids, whereas In may occupy tetrahedral and octahedral voids in the same structure. A survey of the existing ZnInS structures has been extended to indicate all the conceivable hexagonal ZnInS types not yet known.