The γ-ray spectrum resulting from the decay of 16.1-day Rh99 to the excited states of Ru99 has been investigated using Ge(Li) solid-state detectors. The source, produced by the Ru99(p, n)Rh99 reaction using enriched Ru99 metal, was found to emit a large number of γ rays. The energies of the stronger γ rays (with their relative intensities) are: 89.4 (100), 175.2 (7.6), 322.4 (21.7), 353.0 (107.1), 442.8 (5.7), annihilation radiation (30), 527.7 (132.0), 618.0 (13.1), 941.5 (5.0), 1292.1 (1.2), 1532.9 (1.8), 1572.4 (7.7), and 1970.3 (0.5) keV. A number of lines not previously reported have been found. Coincidence measurements and γ-γ directional correlations have been performed using a 6-cc Ge(Li) detector in conjunction with a gain-stabilized NaI(Tl) spectrometer. The decay scheme has been constructed with the aid of coincidence studies and high-precision γ-ray energy measurements. The spin of the 618.0-keV level has been shown to be 1/2 , whereas the results of the 89.4-353.0 and the 175.2-353.0-keV correlations indicate either a 1/2 or 32 assignment to the 442.8-keV level. Attempts to find a theoretical model which represents the experimental data have been made, incorporating the Nilsson model, the intermediate-coupling model of Bohr and Mottelson, and the core-excitation model of de-Shalit.