[en] In a search for intermediate structure, neutron time-of-flight spectra corresponding to 1 and 4 MeV capture γ-ray thresholds were measured for the target isotopes ¹⁸⁵¹⁸⁷Re. The data were analyzed from the point of view of level spacings as well as intermediate structure. A method was developed for estimating the neutron widths of the resonances even in those cases where the neutron widths are comparable to the γ-widths. On the basis of this analysis it was decided which resonances were most likely to be due to p-wave capture. While some unusual behavior was observed, there is no conclusive evidence for intermediate structure. The statistics of level spacings agree with the long range ordering described in the theory of Dyson and Mehta, and are inconsistent with an uncorrelated Wigner distribution. Energies, estimated neutron widths and p-wave probabilities (if over 10%) for 488 resonances in ¹⁸⁵Re and 335 resonances in ¹⁸⁷Re are tabulated for the energy range 24 eV to 2 keV. (Auth.)