The equatorial heavily cratered uplands of Mars are dissected by two classes of small valleys that are intimately associated in compound networks. Pristine valleys with steep valley walls preferentially occupy downstream portions of compound basins. Degraded valleys with eroded walls are laterally more extensive and have higher drainage densities than pristine valleys. Morphometric and crater-counting studies indicate that relatively dense drainage networks were emplaced on Mars during the heavy bombardment about 4.0 b.y. ago. Over a period of approximately 108 years, these networks were degraded and subsequently invaded by headwardly extending pristine valleys. The pristine valleys locally reactivated the compound networks, probably through sapping processes dependent upon high water tables. Fluvial activity in the heavily cratered uplands generally ceased approximately 3.8--3.9 b.y. ago, coincident with the rapid decline in cratering rates. The relict compound valleys on Mars are morphometrically distinct from most terrestrial drainage systems. The differences might be caused by a Martian valley formation episode characterized by hyperaridity, by inadequate time for network growth, by very permeable rock types, or by a combination of factors.