Major nuclear data libraries exhibit some discrepancies for the neutron capture reactions (235)U(n,gamma) and (238)U(n,gamma) at keV energies. These differences reflect also the scatter of experimental data that are primarily based on time-of-flight measurements (TOF) with detection of prompt gamma-rays. We report here on an independent approach for studying such reactions: Neutron activations with subsequent accelerator mass spectrometry (AMS) measurement represent an independent technique, where interference from fission is completely excluded. Activations of natural uranium samples were performed with cold neutrons (Budapest), thermal (Vienna) and with neutrons of 25 and 500 keV (Karlsruhe) for the measurement of (235)U(n,gamma) and (238)U(n,gamma). The produced long-lived (236)U and the decay product of (239)U, (239)Pu, respectively, were subsequently counted by AMS at the Vienna Environmental Research Accelerator. This method for measuring the neutron capture cross section has the advantage that the involved systematic uncertainties are in no way correlated with those inherent to the TOF technique. Preliminary data for these neutron energies indicate good agreement with evaluations and seem to support in the keV energy range the reported lower cross-section values for both capture reactions.