A new activation technique has been developed for the measurement of the ratio of the capture cross section of 238U and the fission cross section of 235U in zero-energy fast reactors. This work was initiated because of the long-standing discrepancy between calculated values of this ratio and radio-chemically measured values. The new technique is a direct counting method that does not involve chemical separation in any way. Measurements have been made in four Z PR-III fast reactor assemblies, two with hard spectra and two with soft spectra. In all four cases the measured ratio was slightly higher than the calculated value being, on the average, 4% higher than calculation. This is in strong contrast with the past radiochemical measurements in Z PR-U3 assemblies that gave values 16% less than calculation. The present measurements, therefore, support the general correctness of the calculated ratio and, hence, indicate that there are no gross errors in the assumed average microscopic values of the 238U capture cross section and the 235 U fission cross section.