Melting and subsolidus relations in the system K₂SO₄MgSO₄CaSO₄ were studied using heating-cooling curves, differential thermal analysis, optics, X-ray diffraction at room and high temperatures and by quenching techniques. Previous investigators were unable to study the binary MgSO₄CaSO₄ system and the adjacent area in the ternary system because of the decomposition of MgSO₄ and CaSO₄ at high temperatures. This problem was partly overcome by a novel sealed-tube quenching method, by hydrothermal synthesis, and by long-time heating in the solidus. As a result of this study, we found: (1) a new compound, CaSO₄·3MgSO₄ (m.p. 1201°C) with a field extending into the ternary system; (2) a high temperature form of MgSO₄ with a sluggishly reversible inversion. An X-ray diffraction pattern for this polymorphic form is given; (3) the inversion of β-CaSO₄ (anhydrite) to α-CaSO₄ at 1195°C, in agreement with grahmann; ⁽¹⁾ (4) the melting point of MgSO₄ is 1136°C and that of CaSO₄ is 1462°C (using sealed tube methods to prevent decomposition of the sulphates); (5) calcium langbeinite (K₂SO₄·2CaSO₄) is the only compound in the K₂SO₄CaSO₄ binary system. This resolved discrepancies in the results of previous investigators; (6) a continuous solid solution series between congruently melting K₂SOP₄·2MgSO₄ (langbeinite) and incongruently melting K₂SO₄·2CaSO₄ (calcium langbeinite); (7) the liquidus in the ternary system consists of primary phase fields of K₂SO₄, MgSO₄, CaSO₄, langbeinite-calcium langbeinite solid solution, and CaSO₄·3MgSO₄. The CaSO₄ field extends over a large portion of the system. Previously reported fields for the compounds (K₂SO₄·MgSO₄·nCaSO₄), K₂SO₄·3CaSO₄ and K₂SO₄·CaSO₄ were not found; (8) a minimum in the ternary system at: 740°C, 25% MgSO₄, 6% CaSO₄, 69% K₂SO₄; and ternary eutectics at 882°C, 49% MgSO₄, 19% CaSO₄, 32% K₂SO₄; and 880°, 67·5% MgSO₄, 5% CaSO₄, 27·5% K₂SO₄.