The paper is concerned with a selection of problems of fluid mechanics which are related to one another by their relevance to a possible hypersonic aircraft. This is regarded as a new type of aircraft, still to be developed, in a series of existing types (classical, swept, and slender). Its main aerodynamic characteristics are that the means for providing volume, lift, and propulsion, all produce shock waves in the air during the high-speed phase of flight, and that the type of flow changes with flight speed. Flow fields of lifting bodies with contained shock waves are considered; they are generally of the mixed type in the sense that they contain elliptic and hyperbolic regions. Friction, heating and transition effects in the generally three-dimensional boundary layers are particularly important. Propulsion by heat addition to an airstream is another characteristic feature and the combined flow field of a lifting propulsive body travelling at hypersonic speeds is discussed with a view to recognizing the aerodynamic problems that matter most. It appears that there is a large field of work with possible and promising practical applications, in which the emphasis lies on problems of perfect-gas-dynamics. The relevant Mach-number range extends up to another as yet unknown, boundary beyond which energy-consuming real-gas effects dominate the flow; it probably extends far enough to cover all that may be required for global transport operations.