AbstractDischarge exceedance probabilities are calculated for a simple model karst aquifer composed of a few multilevel conduits with recharge from a single sinking stream with an exponential flow exceedance distribution. It is assumed that outflow instantaneously matches inflow, so that the conduit volume is constant but discharge is governed by the head in a volumeless shaft at the top end of the system. It is shown that small single conduit aquifers will frequently overflow at the surface during floods and the exceedance probability of flow through the aquifer and over the surface can be defined as a function of the inflow distribution and the form of the aquifer. Systems with multiple conduits will overflow less frequently, but each conduit will exhibit a flow distribution characteristic of its form and position in the vertical hierarchy. Comparison of these findings with actual flow data from a conduit aquifer shows that the approach is valid, although imprecise. The model is unlikely to be applied directly, as it requires unusually detailed data. However, it provides for the first time an indication of typical flow durations for surface overflows and individual conduits in a karst aquifer. Contrasts in flow duration will have a profound influence on solutional and sedimentary processes in the karst system.