Simultaneous measurements of the neutron fission and capture cross sections of 235U have been performed at the Oak Ridge Electron Linear Accelerator for neutrons with energies between 8 eV and 10 keV. These cross sections were measured relative to the shape of the standard 10B(n,α) reaction cross section, and normalized to the Oak Ridge National Laboratory-Rensselaer Polytechnic Institute data between 100 and 200 eV. The comparison of the present 235U capture cross section with the values from other available sources shows that below 200 eV there is general agreement within an error band of ±5%. In the keV energy region, the average difference observed rises to ±12%. The fission cross-section results presented here agree with a worldwide compilation of fission data typically within a 3% error in the entire range of neutron energies investigated in this work. The values of alpha, capture-to-fission ratio, exhibit a remarkable amount of structure.