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Abstract The melting of ice and the subsequent production of regelation ice from the melt water in a large-scale closed system beneath sub-polar and polar glaciers produces progressive fractionation between the melt water and the regelation ice derived from it. A theory is developed which predicts the change of isotopic composition in regelation ice in a subglacial zone of freezing and in the water from which it is derived. The theory is tested against data from the Byrd Station bore hole in West Antarctica, and applied to explain features of the isotopic composition in several other glaciers where thick sequences of regelation ice have formed. The principal conclusions are: 1. Basal isotopic profiles can be used to reconstruct important features of a glacier’s hydrological system. 2. Isotopic profiles in basal regelation ice do not simply reflect isotopic characteristics of ancient atmospheres but also, by using the theory, some of the isotopic characteristics of the normal glacier ice which was destroyed by melting and subsequently produced regelation ice can be reconstructed. Basal regelation ice at Byrd Station reflects an original ice source isotopically colder than the overlying normal ice, and may have formed during the penultimate glacial period, equivalent to stage 6 of the oceanic record. 3. The subglacially derived debris typically found in basal regelation ice gives a complex strain response to a changing pattern of stresses produced by flow over an irregular subjacent bed. Thus, complex tectonic structures in this ice produce highly variable isotopic profiles. However, its gross isotopic characteristics can still be used to reconstruct some of its history. A sharp change in isotopic values tends to occur at the upper limit of basal regelation ice, the nature of which depends on the style and thickness of tectonic disturbance. 4. Isotopic profiles in basal ice can be used to distinguish normal glacier ice from regelation ice, and give strong support to the view that regelation is the major process by which debris is incorporated into the base of a glacier.