The proposed research is directed at the development of new optical interference coatings having low film stress and high reflectance in the X-ray band from 0.1 to 10 keV, which are critically needed for the construction of lightweight, nested X-ray telescopes having high collecting area and sub-arcsecond resolution for Lynx, the high-energy flagship mission under consideration for the 2020 Astrophysics Decadal Survey, as well as for other future NASA X-ray missions. Iridium-based coatings provide high reflectance over the Lynx energy band, however such films also have exceedingly high stress, and film stress deforms thin-shell mirror substrates, thereby degrading telescope angular resolution. The proposed effort aims to develop low-stress, high-X-ray-reflectance optical interference coatings for Lynx, using in place of iridium (Ir) either platinum or tungsten layers, in combination with layers of various light elements. These non-Ir interference coatings have the potential for lower stress and higher reflectance than Ir coatings, thus enabling the realization of lightweight X-ray telescopes having high collecting area and sub-arcsecond angular resolution. Potential NASA Applications The low-stress, high-reflectance X-ray coatings that we propose to develop are critically needed for the construction of light-weight X-ray telescopes having sub-arcsecond angular resolution, as required for NASAs Lynx mission now under consideration for the 2020 Astrophysics Decadal Survey, and for other future missions as well. Potential Non-NASA Applications The new X-ray coatings potentially can be used to develop high-resolution X-ray optics for a variety of other applications outside of space science, including instruments for next-generation light sources (FELs, etc), plasma physics, atto-second physics, and others.