Widespread, several-kilometer-thick successions of layered deposits occur as mounds that partly fill the troughs or chasmata that compose the Valles Marineris on Mars. Like terrestrial subice volcanoes, the layered deposits occur in a volcano-tectonic setting within basins that may have held ponded water or ice. On the basis of their dimensions, morphologies, and associated catastrophic floods and other geologic events as shown in Viking and new Mars Global Surveyor (MGS) data sets, we suggest that the interior deposits are volcanic in origin and possibly generated by subice eruptions. A tuya origin for the mounds can explain the lack of external sediment, mound heights that can rival the plateau, local flat-topped mesas, morphologically distinct mounds of different ages, horizontal to steep dips, fine-grained materials, indications of rare volcanic vents and lava flows, and spectral composition. The extremely diverse layering of west Candor Chasma and possible volcanic cones in Melas may have formed by related subaerial eruptions. Consistent with the suggestion that interior deposits are eroding out of the wall rock, some deposits could have been erupted from sites along the walls.