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To make decisions regarding the use and management of groundwater, understanding the controls of radionuclide mobility is critical. In the southern foreland of a granitic outcrop in Hungary, high gross alpha activity concentration was measured in drinking water wells, related probably to the presence of uranium. It has been suggested that understanding of the groundwater flow system may be a key aspect to understand uranium mobility in groundwater. The goal of the present work was to elucidate the conceptual model of radionuclide mobility in the study area, focusing in particular on the geochemical controls of uranium. For this purpose, water samples were collected and nuclide-specific measurements for 226Ra and radon isotopes were carried out, in addition to 234U+238U measurements, to increase the range of radionuclides and better understand their mobility. A geochemical modeling analysis involving redox-controlling kinetic reactions and a surface complexation model was developed to support the conceptual model. The results from the sampling indicate that excess of 234U+238U (3–753 mBq L−1) contribute to the natural radioactivity measured in drinking water to a large degree. 226Ra was measured in relatively low activity concentrations (<5–63 mBq L−1) with the exception of three specific wells. Notable radon activity concentration was measured in the springwaters from Velence Hills (1.01–3.14 × 105 mBq L−1) and in interrelation with the highest (285–695 mBq L−1) 226Ra activity concentrations. The geochemical model suggests that uranium distribution is sensitive to redox changes in the aquifer. Its mobility in groundwater depends on the residence time of groundwater compared to the reaction time controlling the consumption of oxidizing species. 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