Airfoils operating in the unexplored high-Mach—low-Reynolds number regime are computationally investigated. The motivations are 1) quantificatio n of achievable airfoil performance levels; 2) quantificatio n of parameter sensitivities which impact vehicle sizing; 3) identification of possible shortcomings in the computational methods employed; and 4) identification of test data required for adequate validation of the airfoil designs and performance prediction methods. The investigation centers on candidate airfoils developed for proposed ultrahigh altitude aircraft (UHAA) having both a high-ceiling and a long-range requirement. Computational studies indicate that 35-km ceiling performance at M — 0.60, Re — 200,000 hinges on the effective use of transonic flow to enhance transition and reduce separation-bubble losses. The separation bubbles become associated with large lambda shock structures at the highest tolerable Mach numbers. Airfoil performance predictions are parameterized by quantities dependent only on altitude and vehicle characteristics, and independent of flight trim conditions. For the airfoils designed, no flaps are necessary to achieve nearly optimal performance at both 35-km ceiling conditions as well as lower 15-25-km altitudes where long-range cruise would occur. Variation in airfoil thickness between 11-15% has surprisingly little impact on aerodynamic performance.