Measurements of the energy spectra of delayed neutrons for the isotope-separated, fission product precursors 93-97Rb and 143-145Cs, over the energy region from ∼10 to ∼1300 keV, are reported. These data were obtained at the TRISTAN ISOL facility using gas-filled proton-recoil proportional counters. The data for each of the rubidium and cesium isotopes show good qualitative agreement with the existing 3He ionization chamber data at energies above ∼200 keV. In addition, they provide definitive spectral information down to ∼10 keV. Of particular note is the observation of line structure below ∼200 keV with energy resolution much better than that obtained using 3He ionization chambers.