Neutron capture by the heavier stable ruthenium isotopes and by natural rhodium has been measured at the Oak Ridge Electron Linear Accelerator time-of-flight facility up to 500 to 700 keV. Most of these isotopes are important as fission products. Strength functions S0, S1, S2, and Sγ were fitted to the average cross sections derived for the pure isotopes up to 113 keV. Resonance parameters were fitted for ∼100 cross-section peaks for each isotope.