Precision Segmented Reflector (PSR) technology is currently being developed for a range of future applications such as the Large Deployable Reflector (LDR). This paper outlines the structures activities at NASA Langley Research Center in support of the PSR program. Design concepts are explored for erectable and deployable support structures which are envisioned to be the backbone of these precision reflectors. Important functional requirements for the support trusses related to stiffness, mass, and surface accuracy are reviewed. Proposed geometries for these structures and factors motivating the erectable and deployable designs are discussed. Analytical results related to stiffness, dynamic behavior, and surface accuracy are presented and considered in light of the functional requirements. Results are included for both a 4-meter-diameter prototype support truss which is currently being designed as the Test Bed for the PSR technology development program, and for two 20-meter-diameter support structures. For the most likely ground support conditions, the maximum gravity-induced deflection of the Test Bed support truss (with 10 kg/m2 panels) was determined to be approximately 50 μm, and the rms surface error was 12 μm. For the same support conditions, the Test Bed fundamental frequencies were between 30 Hz and 40 Hz. It is shown that if the secondary optical system is supported by a simple tripod design, the first six vibration modes are likely to be dominated by the secondary system. The 20-meter-diameter support trusses were found to be quite stiff for structures of such large size, having maximum deflections on the order of 0.35 mm in a 1-g environment. When considered as part of a reflector system, these support trusses had maximum deflections of 6-11µm under slewing loads, and free-free fundamental frequencies of 6-8 Hz.