The phase diagram of the system Li 2S/Na 2S/S has been investigated at 400°C. In the sulphur-rich part of the ternary diagram, two liquid phases exist; one of these is nearly pure liquid sulphur, and the other is an alkali metal polysulphide melt. When sulphur is removed, the polysulphide remains as a single liquid phase. The composition limits of the two-liquid region have been determined by equilibrating the two liquid phases, quenching the analysing. If more sulphur is removed from the polysulphide melt, solid phases eventually separate. The composition boundary the polysulphide liquid and the (one liquid, one solid) region of the diagram has been determined, by separating the phases using high temparature centrifuge and subsequent analysis. For all Li/Na ratios between 100/0 and 20/80, the solid phase separating is Li 2S; in the pure sodium system, it is Na 2S 2. No evidence was found for solid lithium polysulphides or for solid phases containing both sodium and lithium. The significance of this diagram with respect to the properties of a hypothetical (sodium,lithium)-sulphur cell is discussed.