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Mobility of naturally occurring U-238 and U-234 radionuclides was studied in a low permeability, reducing claystone formation (Opalinus Clay) near its contact with an overlying oxidising aquifer (Dogger Limestones) at Mont Terri, Switzerland. Our data point to a limited redistribution of U in some of the studied samples. Observed centimetre-scale U mobility is explained by slow diffusive transport of U-234 in the pore waters of the Opalinus Clay driven by spatially variable in situ supply (by alpha-recoil) of U-234 from the rock matrix. Metre-scale mobility is interpreted as a result of infiltration of meteoric water into the overlying aquifer which developed gradients of U concentration across the two rock formations. This triggered a slow in-diffusion of U with (U-234/U-238) > 1 into the Opalinus Clay as attested by a clear-cut pattern of decreasing bulk rock (U-234/U-238) inwards the Opalinus Clay, away from the Dogger Limestones.