Vibrational spectroscopy has been used to investigate the room-temperature high-pressure phases of the energetic material hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX). The pressure-induced alterations in the spectral profiles were studied in a compression sequence to 30.2 GPa using Raman spectroscopy and to 26.6 GPa using far-infrared spectroscopy. At pressures near 4.0 GPa, several changes become immediately apparent in the Raman spectrum, such as large frequency shifts, mode splittings, and intensity changes, which are associated with a phase transition from alpha-RDX to gamma-RDX. Our study extends the kinetic stability of gamma-RDX to pressures near 18.0 GPa. Evidence for a new phase was found at pressures between 17.8 and 18.8 GPa and is based on the appearance of new vibrational bands and associated changes in intensity patterns. The new phase has vibrational characteristics that are similar to those of beta-RDX, suggesting the two polymorphs share a related crystal structure.