Acid sulfate wall-rock alteration, characterized by the assemblage alunite + kaolinite + quartz + or - pyrite, results from base leaching by fluids concentrated in H ₂ SO ₄ . Requisite amounts of H ₂ SO ₄ can be generated by different mechanisms in three principal geologic environments: (1) by atmospheric oxidation of sulfides in the supergene environment, (2) by atmospheric oxidation at the water table in the steam-heated environment of H ₂ S released by deeper, boiling fluids, and (3) by the disproportionation of magmatic SO ₂ to H ₂ S and H ₂ SO ₄ during condensation of a magmatic vapor plume at intermediate depths in magmatic hydrothermal environments in silicic and andesitic volcanic terranes. In addition, coarse vein alunite may form in a magmatic steam environment from rapid release of an SO ₂ -rich magmatic vapor phase at high temperature and low pressure or from the oxidation of a more reduced magmatic vapor by entrained atmospheric oxygen in the carapace of a volcanic edifice.Alunite [KAl ₃ (SO ₄ ) ₂ (OH) ₆ ] contains four stable isotope sites and complete analyses (delta D, delta ¹⁸ O (sub SO ₄ ) , delta ¹⁸ O _OH , and delta ³⁴ S) are now possible. Except for delta ¹⁸ O _OH in magmatic hydrothermal alunites, primary values are usually retained. In cooperation with many colleagues, over 500 measurements have been made on nearly 200 samples of alunite and associated minerals from 23 localities, and 55 additional analyses have been taken from the literature. This survey confirms that kinetic factors play an important role in the stable isotope systematics of alunite and acid sulfate alteration. To a very large extent they form the isotopic basis for distinguishing between environments of acid sulfate alteration, and they provide important insights into attendant processes. Stable isotope analyses of alunite, often in combination with those on associated sulfides and kaolinite, permit recognition of environments of formation and provide information on origins of components, processes (including rates), physical-chemical environments, and temperatures of formation.Supergene acid sulfate alteration may form over any sulfide zone when it is raised above the water table by tectonics or exposed by erosion. It may overprint earlier acid sulfate assemblages, particularly the magmatic hydrothermal assemblages which are pyrite rich such as at El Salvador, Chile; Rodalquilar, Spain; and Goldfield, Nevada. Supergene alunite normally has delta ³⁴ S values virtually identical to precursor sulfides unless bacteriogenic reduction of aqueous sulfate takes place in standing pools of water. delta D values are close to that of local meteoric water unless extensive evaporation occurs. delta D and delta ¹⁸ O _OH values of supergene alunites from a range of latitudes fall in a broad zone parallel to the meteoric water line much the way delta D and delta ¹⁸ O values of associated halloysite-kaolinite fall near the kaolinite line of Savin and Epstein (1970). delta ¹⁸ O (sub SO ₄ ) values are kinetically controlled and will reflect the hydro-geochemistry of the environment. delta ¹⁸ O (sub SO ₄ -OH) alues are grossly out of equilibrium and large negative values are definitive of a supergene origin.In steam-heated environments, such as those at the Tolfa district, Italy, and Marysvale, Utah, and numerous modern geothermal systems, acid sulfate alteration zones are characterized by pronounced vertical zoning. Such acid sulfate alteration may occur over adularia-sericite-type base and precious metal ore deposits such as the one at Buckskin, Nevada. Initial delta ¹⁸ O (sub SO ₄ ) and delta ³⁴ S values are kinetically controlled, but delta ¹⁸ O (sub SO ₄ ) values usually reach equilibrium with fluids, and even delta ³⁴ S values may reflect partial exchange with H ₂ S where the residence time of aqueous sulfate is sufficient. Most alunites of steam-heated origin have delta ³⁴ S values the same as those of precursor H ₂ S (and as related sulfides, if present) and delta D values similar to that of local meteoric water. In the samples analyzed, most delta ¹⁸ O (sub SO ₄ -OH) values give reasonable temperatures of 90 degrees to 160 degrees C, indicating that delta ¹⁸ O (sub SO ₄ ) and delta ¹⁸ O _OH values reflect a close approach to equilibrium with the fluid. The delta ¹⁸ O (sub SO ₄ ) and delta ¹⁸ O _OH values also reflect the degree of exchange of the meteoric fluids with wall rock. Coeval kaolinites typically have delta ¹⁸ O and delta D values to the left of the kaolinitc line.Magmatic hydrothermal, acid sulfate alteration zones in near-surface epithermal deposits such as Summitville, Colorado. Julcani, Peru, and Red Mountain and Lake City, Colorado, are characterized by vertical orientation and horizontal zoning, the presence of coeval pyrite, PO ₄ analogues of alunite, zunyite, and later gold, pyrite and enargite, and often other Cu-As-Sb-S minerals. Acid sulfate alteration assemblages also occur as late stages in the porphyry-copper deposit at E1 Salvador, Chile. In the examples studied, magmatic hydrothermal alunites have delta D values close to those for magmatic water. delta ³⁴ S values are 16 to 28 per mil larger than those for associated pyrite, reflecting equilibrium between aqueous H ₂ S and SO ₄ formed by the disproportionation of magmatically derived SO ₂ . delta ¹⁸ O (sub SO ₄ ) values are usually 8 to 18 per mil and vary systematically with delta ³⁴ S values, reflecting variations in temperature and/or H ₂ S/SO ₄ fluid ratios. Further variation in delta ¹⁸ O (sub SO ₄ ) values may result if SO ₂ condenses in mixed magmatic meteoric water fluids. delta ¹⁸ O (sub SO (sub 4-) OH) values of magmatic hydrothermal alunites are generally unsuitable for temperature determinations because of retrograde exchange in the OH site, but delta ³⁴ S (sub alunite-pyrite) values provide reliable temperature estimates.Magmatic steam environments appear to occur over a range of depths and are characterized by monomineralic veins of coarse alunite in variably alunitized and kaolinized wall rocks containing minor pyrite. Alunite formed in the magmatic steam environment can usually be recognized by delta ³⁴ S near delta ³⁴ S (sub Sigma S) values and delta D and delta ¹⁸ O (sub SO ₄ ) values near magmatic values. Magmatic steam alunite differs from magmatic hydrothermal alunite by having delta ³⁴ S close to delta ³⁴ S (sub Sigma S) values of the system. delta ¹⁸ O (sub SO (sub 4-) OH) values of most magmatic steam alunite give temperatures ranging from 90 degrees to 210 degrees C but, for reasons which are not understood, some temperatures as well as calculated delta ¹⁸ O (sub H ₂ O) values are too low for presumed precipitation from a magmatic vapor phase. Magmatic steam environments may occur over porphyry-type mineralization as at Red Mountain, Colorado, and Alunite Ridge, Utah, and over or adjacent to adularia-sericite-type deposits in volcanic domes as at Cactus, California.