Measurement of the energy spectra of delayed neutrons for the isotope-separated, fission product precursors 87Br, 88Br, 89Br, 90Br, 137I, 138I, 139I, and 136Te are reported for an energy range up to 1213 keV and with lower cutoff energies of 11.1, 11.1, 29.9, 48.9, 14.2, 23.3, 29.9, and 48.9 keV, respectively. These data were obtained at the TRISTAN Isotope Separation On-Line facility using H2 and CH4 gas-filled proportional counters. The data for each of the bromine, iodine, and tellurium isotopes show good qualitative agreement with the published 3He ionization chamber data at energies above ∼200 keV. In addition, they provide definitive spectral information down to their respective cutoff energies.