The geomorphology of the martian valley networks is examined from a hydrological perspective for the compatibility with an origin by rainfall, globally higher heat flow, and localized hydrothermal systems. Comparison of morphology and spatial distribution of valleys on geologic surfaces with terrestrial fluvial valleys suggests that most martian valleys are probably not indicative of a rainfall origin, nor are they indicative of formation by an early global uniformly higher heat flow. In general, valleys are not uniformly distributed within geologic surface materials as are terrestrial fluvial valleys. Valleys tend to form either as isolated systems or in clusters on a geologic surface unit leaving large expanses of the unit virtually untouched by erosion. With the exception of fluvial valleys on some volcanoes, most martian valleys exhibit a sapping morphology and do not appear to have formed along with those that exhibit runoff morphology. In contrast, terrestrial sapping valleys form from and along with runoff valleys. The isolated or clustered distribution of valleys suggests localized water sources were important in drainage development, Persistent groundwater outflow driven by localized, but vigorous hydrothermal circulation associated with magmatism, volcanism, impacts, or tectonism is, however, consistent with valley morphology and distribution, Snowfall From sublimating ice-covered lakes or seas may have provided an atmospheric source of water for the formation of some valleys in regions where the surface is easily eroded and where localized geothermal/hydrothermal activity is sufficient to melt accumulated snowpacks. (C) 2001 Elsevier Science B.V. All rights reserved.