Neutron spectra have been measured by the time-of-flight method from 1 eV to 2 keV at various positions across depleted uranium and borated polyethylene in slab geometry with an energy resolution of 0.9% at 6.68 eV. The observed behavior around the 6.68-eV resonance in 238U has been compared with the predictions of the transport theory code 1DF in S4 and S6 approximations using different quadratures and spatial representations. The space-averaged flux has been calculated with the slowing down code GAROL. The 1DF calculations agree reasonably well with experiment and the GAROL values.