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Occurrence of flooding because of rainfall and snowmelt, and also mechanisms of formation of runoff are the problems waiting for their research. In modern settings for this purpose there would be useful to use the mathematical methods at the description of these mechanisms. Here the review of the results which are available on this problem now is given. The basic concepts and corresponding mathematical models are given too. The most advanced theoretical results on mathematical modelling of rainfall-runoff problems is given in stochastic settings. Furthermore are described the approaches for...