Copolymerization or blending of a polymer with polyhedral oligomeric silsesquioxane (POSS) or incorporating siloxane into a polymer backbone can yield a material that resists AO attack in low Earth orbit (LEO) through the formation of a passivating silicon-oxide layer. Still, these hybrid organic/inorganic polymers may become rough through AO reactions as the passivating layer is forming. Surface roughness may enhance satellite drag by promoting energy transfer and scattering angle randomization during gas-surface collisions. As potential low-drag and AO-resistant materials, we have investigated three types of polymer films: (1) CORIN, a colorless polyimide that is a copolymer with POSS, (2) Novastrat 905, a polyimide blended with trisilanolphenyl POSS, and (3) BSF-30, a commercial siloxane/polyimide block chain copolymer from NIPPON STEEL Chemical & Material. Some films of CORIN and POSS-Novastrat were prepared with 10 nm thick Al2O3 coatings that were grown by atomic layer deposition (ALD). All materials were exposed to AO fluences near 1×1021 O-atoms cm-2 in a ground-based hyperthermal AO beam facility and on the International Space Station (MISSE-17 and MDM2). Coated CORIN, coated POSS-Novastrat, and BSF-30 had extremely low erosion yields, <1% that of Kapton H, and their surfaces remained relatively smooth. Uncoated CORIN and uncoated POSS-Novastrat etched slightly (3-6% the erosion yield of Kapton H), and the POSS-Novastrat surface became rough. XPS analysis indicated that a silica layer was formed on the all the uncoated surfaces, whereas the ALD-coated films showed no apparent change from AO attack. The AO effects resulting from lab and LEO exposures were very similar, with the exception of yellowing on the LEO-exposed CORIN sample, suggesting a higher VUV dose in LEO. The very low erosion yields of the materials and the smoothness of their surfaces (except POSS-Novastrat) make these materials good candidates for low-drag, AO-resistant materials for use in very low Earth orbit.