Abstract Analyses of water-quality variables for the Yarra River in South-Eastern Australia have shown that the relationship between species concentrations in the river and the river discharge is time dependent and non-linear. A simple dynamic model relating the time evolution of the total mass of chemical element in the catchment area to chemical loading in the river provides high-accuracy predictions of Absolute and time-integrated values of the latter. Because the chemical loads in the river are controlled by the total mass of chemical element in the catchment area, the relationship between chemical concentration in stream water and river discharge reveals a hysteresis. A balance between chemical loads in the river and the loads into the catchment area determines the direction of rotation of the hysteresis (clockwise or counter-clockwise). The predominance of either the storm wash-off of chemicals deposited in the catchment area or the dilution by stream water of the loading from constant sources (such as groundwater and/or anthropogenic local emissions of wastes) directly into the river system governs the sign of the relationship (positive or negative).