From the point of view of engineering hydrology, design discharge is one of the most important input data for the needs of dimensioning and planning of hydrotechnical structures. Both, maximum and minimum discharge values represent the input data in the analysis of the effects of water on the environment and human health. Maximum peaks are needed for flood protection, and minimum peaks for the proper action in case of drought. In the master thesis, we determined the design discharge for different return periods using probability analyzes of both maximum and minimum peaks, and three different distribution functions (generalized distributions of extreme values, Pearson III distributions, and log-Pearson III distributions). Uncertainties were also considered, and confidence intervals for individual distribution functions were determined. The analysis is performed for 179 water gauging stations in Slovenia, which have been already analyzed by ARSO in the past with a shorter set of data. In this thesis, we were able to determine the impact of an 8-year longer data set on the values of design discharge. In addition to comparing the results, we calculated and empirically determined the discharge limit values, which were compared with various empirical equations that have already been proposed for Slovenian river basins. We found that an 8-year longer data set affects design discharge, as maximum discharge generally increase (0,1-77 %) and minimum decrease(0,3-96 %). Individual distribution functions remain within confidence intervals. The results show that the longer the time period of operation of the water gauging station, the smaller the difference factor between the upper and lower confidence limit. When comparing the calculated design discharge and the values of empirical equations of different authors, we found that the calculated design discharge in most of the considered river basins do not approach the values of empirical equations. The largest deviations are in the river basins with the smallest catchment areas, for which empirical equations are most often used in practice.