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Understanding planetary landforms, including the theater-headed valleys (box canyons) of Mars, usually depends on interpreting geological processes from remote-sensing data without ground-based corroboration. Here we investigate the origin and development of two Mars-analog theater-headed valleys in the hyperarid Atacama Desert of northern Chile. Previous workers attributed these valleys to groundwater sapping based on remote imaging, topography, and publications on the local geology. We evaluate groundwater sapping and alternative hypotheses using field observations of characteristic features, strength measurements of strata exposed in headscarps, and estimates of ephemeral flood discharges within the valleys. The headscarps lack evidence of recent or active seepage weathering, such as spring discharge, salt weathering, alcoves, or vegetation. Their welded tuff caprocks have compressive strengths multiple times those of the underlying epiclastic strata. Flood discharge estimates of cubic meters to tens of cubic meters per second, derived using the Manning equation, are consistent with the size of transported clasts and show that the ephemeral streams are geomorphically effective, even in the modern hyperarid climate. We interpret that headscarp retreat in the Quebrada de Quisma is due to ephemeral flood erosion of weak Miocene epiclastic strata beneath a strong welded tuff, with erosion of the tuff facilitated by vertical jointing. The Quebrada de Humayani headscarp is interpreted as the scar of a giant landslide, maintained against substantial later degradation by similar strong-over-weak stratigraphy. This work suggests that theater-headed valleys on Earth and Mars should not be attributed by default to groundwater sapping, as other processes with lithologic and structural influences can form theater headscarps. Published by Elsevier Inc.