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Hydrogen peroxide (H2O2) and methyl hydroperoxide (MHP, CH3OOH) serve as HOx (OH and HO2 radicals) reservoirs and therefore as useful tracers of HOx chemistry. Both hydroperoxides were measured during the 2016–2018 Atmospheric Tomography Mission as part of a global survey of the remote troposphere over the Pacific and Atlantic Ocean basins conducted using the NASA DC-8 aircraft. To assess the relative contributions of chemical and physical processes to the global hydroperoxide budget and their impact on atmospheric oxidation potential, we compare the observations with two models, a diurnal steady-state photochemical box model and the global chemical transport model Goddard Earth Observing System (GEOS)Chem. We find that the models systematically under-predict H2O2 by 5%–20% and over-predict MHP by 40%–50% relative to measurements. In the marine boundary layer, over-predictions of H2O2 in a photochemical box model are used to estimate H2O2 boundary-layer mean deposition velocities of 1.0–1.32 cm s −1, depending on season; this process contributes to up to 5%–10% of HOx loss in this region. In the upper troposphere and lower stratosphere, MHP is under-predicted and H2O2 is over-predicted by a factor of 2–3 on average. The differences between the observations and predictions are associated with recent convection: MHP is underestimated and H2O2 is over-estimated in air parcels that have experienced recent convective influence. Plain Language Summary Hydrogen peroxide (H2O2) and methyl hydroperoxide (MHP, CH3OOH) in the atmosphere can act as reservoirs for one of the main drivers of atmospheric chemistry, HOx (HOx = OH and HO2). Both H2O2 and MHP were measured during the 2016–2018 Atmospheric Tomography Mission (ATom), which investigated the atmosphere over the oceans far from direct human influence. The measurements are compared to two types of models to assess our understanding of the chemical and physical processes that control their abundance. We find that these models consistently predict H2O2 to be lower and MHP to be higher than was measured during ATom. We use the discrepancy between the model and the measurements to investigate the role of deposition (removal of compounds from the Earth's atmosphere due to interactions with surfaces and with liquid water) on H2O2 in the lowest portion of atmosphere and the role of convection (vertical transport during storms and other meteorological events) on MHP between 6 and 12 km altitudes.