A theoretical analysis of the exchange of nonsorbing solutes between a permeable streambed and the overlying water of a stream or river is presented in this paper. In a companion paper [Elliott and Brooks, this issue] the results of experimental studies of such exchange are presented. The analysis focuses on water movements into, within, and out of the bed which result from the presence of bed forms (ripples and dunes) and highlights the mechanisms of “pumping” and “turnover.” Pumping is the movement of fluid through the bed induced by steady dynamic pressure variations over bed forms. Turnover occurs as moving bed forms trap and release interstitial fluid. The detailed analysis was used to generate the distribution of the residence time of solute within the bed, which can be used to calculate the net mass exchange due to pumping and turnover.