A theoretical model is described for estimating the impacts of changes in Lake Victoria levels on river flows, lake levels and swamp areas in the upper White Nile basin. The basis of the model is to represent the main river channel by a series of interconnected lakes and swamps, whose water balances are described by differential equations relating outflows to levels, areas and the net basin supply at each point. Closed form solutions are obtained for two situations: (a) a long-term change in the mean level of Lake Victoria, and (b) a return to equilibrium levels following an initial disturbance in Lake Victoria levels. A simple model for the net basin supply to Lake Victoria is also used to relate these changes in levels to changes in climate and runoff in the basin. The results illustrate the extreme sensitivity of White Nile flows to changes in Lake Victoria levels and outflows, and in particular to variations in the direct rainfall on the lake surface. Estimates are also presented for the various time scales and time delays which affect the White Nile system.