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Kovář P., Hrabalíková M., Neruda M., Neruda R., Šrejber J., Jelínková A., Bačinová H. (2015): Choosing an appropriate hydrological model for rainfall-runoff extremes in small catchments. Soil & Water Res., 10: 137–146. Real and scenario prognosis in engineering hydrology often involves using simulation techniques of mathematical modelling the rainfall-runoff processes in small catchments. These catchments are often up to 50 km2 in area, their character is torrential, and the type of water flow is super-critical. Many of them are ungauged. The damage in the catchments is enormous, and the length of the torrents is about 23% of the total length of small rivers in the Czech Republic. The Smědá experimental mountainous catchment (with the Bílý potok downstream gauge) in the Jizerské hory Mts. was chosen as a model area for simulating extreme rainfall-runoff processes using two different models. For the purposes of evaluating and simulating significant rainfall-runoff episodes, we chose the KINFIL physically-based 2D hydrological model, and ANN, an artificial neural network mathematical “learning” model. A neural network is a model of the non-linear functional dependence between inputs and outputs with free parameters (weights), which are created by iterative gradient learning algorithms utilizing calibration data. The two models are entirely different. They are based on different principles, but both require the same time series (rainfall-runoff ) data. However, the parameters of the models are fully different, without any physical comparison. The strength of KINFIL is that there are physically clear parameters corresponding to adequate hydrological process equations, while the strength of ANN lies in the “learning procedure”. Their common property is the rule that the greater the number of measured rainfall-runoff events (pairs), the better fitted the simulation results can be expected.