Natural surficial accumulations of nitrate-rich salts in the Atacama Desert, northern Chile, and in the Death Valley region of the Mojave Desert, southern California, are well known, but despite many geologic and geochemical studies, the origins of the nitrates have remained controversial. N and O isotopes in nitrate, and S isotopes in coexisting soluble sulfate, were measured to determine if some proposed N sources could be supported or rejected, and to determine if the isotopic signature of these natural deposits could be used to distinguish them from various types of anthropogenic nitrate contamination that might be found in desert groundwaters. High-grade caliche-type nitrate deposits from both localities have ??15N values that range from -5 to +5???, but are mostly near 0???. Values of ??15N near 0??? are consistent with either bulk atmospheric N deposition or microbial N fixation as major sources of the N in the deposits. ??18O values of those desert nitrates with ??15N near 0??? range from about +31 to + 50??? (V-SMOW), significantly higher than that of atmospheric O2 (+ 23.5???). Such high values of ??18O are considered unlikely to result entirely from nitrification of reduced N, but rather resemble those of modern atmospheric nitrate in precipitation from some other localities. Assuming that limited modern atmospheric isotope data are applicable to the deposits, and allowing for nitrification of co-deposited ammonium, it is estimated that the fraction of the nitrate in the deposits that could be accounted for isotopically by atmospheric N deposition may be at least 20% and possibly as much as 100%. ??34S values are less diagnostic but could also be consistent with atmospheric components in some of the soluble sulfates associated with the deposits. The stable isotope data support the hypothesis that some high-grade caliche-type nitrate-rich salt deposits in some of the Earth's hyperarid deserts represent long-term accumulations of atmospheric deposition (possibly in the order of 104 yr for the Death Valley region. 107 yr for the Atacama Desert) in the relative absence of soil leaching or biologic cycling. The combined N and O isotope signature of the nitrate in these deposits is significantly different from those of many other natural and anthropogenic sources of nitrate.