The EPR spectra of RbMgBr3 crystals doped with Mn2+, Cr3+ and Gd3+ indicate that the host lattice undergoes two structural phase transitions between the melting point and 77K. At high temperatures, 738-449K, RbMgBr3 adopts the hexagonal CsNiCl3 structure which consists of identical symmetric (MgBr3-)n chains (phase I). At intermediate temperatures, 449-235K, the structure appears to contain two structurally distinct types of (MgBr3-)n chains (phase II). The spectral properties indicate that one type of chain is polar while the other is non-polar (symmetric). At low temperatures, 228-77K, the lattice is no longer hexagonal and seems to consist of a single type of polar (MgBr3-)n chain (phase III). The first phase transformation is quite abrupt while the second transformation takes place over an appreciable temperature range ( approximately 7K).