Of the six stable isotopic variants of O2, only three are measured routinely. Observations of natural variations in 16O18O/16O16O and 16O17O/16O16O ratios have led to insights in atmospheric, oceanographic, and paleoclimate research. Complementary measurements of the exceedingly rare 18O18O and 17O18O isotopic variants might therefore broaden our understanding of oxygen cycling. Here we describe a method to measure natural variations in these multiply substituted isotopologues of O2. Its accuracy is demonstrated by measuring isotopic effects for Knudsen diffusion and O2 electrolysis in the laboratory that are consistent with theoretical predictions. We then report the first measurements of 18O18O and 17O18O proportions relative to the stochastic distribution of isotopes (i.e., Δ36 and Δ35 values, respectively) in tropospheric air. Measured enrichments in 18O18O and 17O18O yield Δ36 = 2.05 ± 0.24‰ and Δ35 = 1.4 ± 0.5‰ (2σ). Based on the results of our electrolysis experiment, we suggest that autocatalytic O(3P) + O2 isotope exchange reactions play an important role in regulating the distribution of 18O18O and 17O18O in air. We constructed a box model of the atmosphere and biosphere that includes the effects of these isotope exchange reactions, and we find that the biosphere exerts only a minor influence on atmospheric Δ36 and Δ35 values. O(3P) + O2 isotope exchange in the stratosphere and troposphere is therefore expected to govern atmospheric Δ36 and Δ35 values on decadal timescales. These results suggest that the ‘clumped’ isotopic composition of atmospheric O2in ice core records is sensitive to past variations in atmospheric dynamics and free-radical chemistry.