Ephemeral flow in arid lands in characterized by alternating random periods of wetness and dryness. Sustained flow occurs only in those aridland watersheds fed by snowmelt, large aquifers, reclaimed waste waters, or during sustained periods of rainfall. Stochastic analysis of flows focuses on properties of flow duration, temporal distribution of flow within a single wet period and within a long wet-dry sequence, antecedent dry periods, and flow volumes. Analysis is a prelude to the synthesis of models of ephemeral flow. The purpose of this paper is to present the recent results in the stochastic analysis of ephemeral flows in the metropolitan area of Tuscon and to propose a framework for future analyses of such data.