Eutrophication management is a more complicated task in running waters than in lakes and reservoirs, as network topology and longitudinal transport modulate system response to nutrient supply through dilution and short water residence time. The paradigm of lake eutrophication management is to force nutrient limitation of algal biomass by the reduction of nutrient loads. In streams, however, application of this paradigm was obviously unsuccessful in many cases, while it worked in others. Complex catchment modelling revealed that proliferation of phytoplankton in streams required the coincidence of three independent factors: adequately high nutrient supply, an inoculum of algae from the upstream environment, and a suitable downstream hydromorphology that provides sufficiently long time for algal growth. Standing water bodies in the stream network are not optimal habitats for fluvial algae and may disrupt phytoplankton development along the flow. At the same time, algae adapted to standing water conditions get washed out into the streams and may temporarily determine the trophic status of the downstream network. These phenomena suggest that eutrophication at the basin level is determined by the interaction of various factors, so its modelling requires a complex approach. The application of detailed, dynamic eutrophication models in large river basins needs immense amounts of data and computational power. To overcome this obstacle, we elaborated a novel, simplified steady-state network eutrophication model that targets to approximately quantify eutrophication potential of rivers in large basins. The model focuses only on the most important drivers of stream eutrophication and its data requirements can be covered from online databases. A case study is presented for the Danube Basin.