Drainage densities on Mars range from zero over large areas of volcanic plains to 0.3--0.5 km-1 locally on some volcanoes. These values refer to geologic units, not to drainage basins, as is normal for terrestrial drainage densities. The highest values are close to the lowest terrestrial values derived by similar techniques. Drainage densities were determined for every geologic unit portrayed on the 1:15,000,000 geologic map of Mars. Except for volcanoes the geologic unit with the highest drainage density is the dissected Noachian plains with a drainage density of 0.0074 km-1. The average drainage density for Noachian units is 0.0032 km-1, for Hesperian units is 0.00047 km-1, and for Amazonian units is 0.00007 km-1, excluding the volcanoes. These values are 2--3 orders of magnitude lower than typical terrestrial densities as determined by similar techniques from Landsat images. The low drainage densities, despite a cumulative record that spans billions of years, indicate that compared with the Earth, the channel-forming processes have been very inefficient or have operated only rarely or that the surface is extremely permeable. The high drainage density on volcanoes is attributed to a local cause, such as hydrothermal activity, rather than to a global cause such as climate change.¿ 1997 American Geophysical Union