The neutron capture cross sections of 56Fe and 58Fe have been measured in the energy range from 10 to 250 keV relative to the gold standard. A pulsed 3-MV Van de Graaff accelerator and the 7Li(p,n) reaction served as a neutron source. Capture gamma rays were detected by two C6D6 detectors, which were operated in coincidence and anticoincidence modes. Two-dimensional data acquisition allowed the offline application of the pulse height weighting technique. The samples were located at a 60-cm flight path. The total time resolution was 1.2 ns allowing an energy resolution of 2 ns/m. The experimental setup was optimized with respect to low background and low neutron sensitivity. The additional 4-cm flight path from the sample to the detector was sufficient to discriminate against the capture of sample scattered neutrons by the additional time of flight. In this way reliable results were obtained even for the strong s-wave resonances of both isotopes. The experimental capture yield was analyzed with the FANAC code. The energy resolution allowed extraction of resonance parameters in the energy range from 10 to 100 keV. Individual systematic uncertainties were found to range between 5 and 10% while the statistical uncertainty is 3 to 5% for most resonances. A comparison to other results exhibits systematic differences of 7 to 11% for 56Fe. The present results for 58Fe differ up to 50% from the only other measurement for this isotope.