The NASA Advanced X-ray Astrophysics Facility-Imaging (AXAF-I), one of NASA's Great Observatories, will be launched in 1998. The AXAF-I High Resolution Mirror Assembly (HRMA) will provide sub-arc second imaging resolution over the expected mission life of five years. During assembly and operational life of the telescope, small dimensional changes of the structural support system can degrade the telescopes resolving power by introducing unwanted forces. The forces that are introduced depend, in part, on the long term temporal dimensional stability of the materials that are used in the telescope. A year-long stability study carried out at the university of Arizona Dimensional Stability Laboratory recently concluded. Cyanate ester-based composites, 7050-T7451 aluminum, LR-35 invar, 6Al-4V titanium, 6061-T6 aluminum and Zerodur were studied. The Zerodur material was found to be stable to better than 0.03 ppm/yr. The titanium was found to be stable to better than 0.5 ppm/yr. The 7050- T7451 aluminum and cyanate ester-based composites were found relatively unstable but their instability improved significantly with time. Monte-Carlo and deterministic techniques were used to predict the effects of the instability on the telescopes' performance. Temporal instability effects were within the systems top level requirements.