We report here the discovery of a basin, which we call the Tyro Basin, in the eastern Mediterranean in which anoxic conditions exist and organic-rich sediments are accumulating. Bottom water samples show extremely high salt concentrations. A horizontal midwater sound reflector about 70 m above the basin floor was observed in a seismic reflection profile across the basin. From shipboard observations we conclude that dissolution of Messinian evaporites, exposed by faulting in the sides of the basin, causes stagnant bottom conditions. This basin provides an opportunity to test some of the hypotheses concerning the formation of sapropels present in cores collected from the same area. Cores taken in an adjacent similar basin (for which we propose the name Kretheus Basin) indicate a recent change from anoxic to oxygenated conditions which was probably caused by tectonic activity associated with the Strabo Trench.