A conceptual water balance model is applied in a distributed structure to model monthly river flow in tributaries of two very large river systems which exhibit non-stationary behaviour, the Paraná in South America and the Niger in West Africa. The approach utilises global data sets of rainfall and potential evaporation (PE) time series and soil available water capacity at 0·5 degree latitude and longitude resolution. River flow data for tributaries ranging in size from 631 to 71 510 km2 for the period 1931–1990 (Paraná) and 1950–1989 (Niger) are used to calibrate and validate the model. The results show varying degrees of model performance during both the calibration and validation procedure. The analysis highlights some interesting issues pertaining to the development and application of water balance models such as sensitivity of model performance and parameter values to input data sets, particularly the method chosen to estimate PE. The paper ends with an analysis of prolonged fluctuation in flow characteristics exhibited by both rivers after the early 1970s, associated with fluctuation in rainfall regime and possibly change in land use or land cover. Between 1931–1971 and 1972–1990 Paraná river flows increased by ∼28% (rainfall increase ∼5%) and between 1950–1969 and 1970–1989 Niger river flows decreased by ∼34% (rainfall decrease ∼14%).