This paper presents a modified nonlinear longitudinal model for an air-breathing hypersonic vehicle and the design of an L 1 adaptive controller for it. It is assumed that the mid-fuselage is a rigid-body, while the aft-fuselage is linearly elastic, and a rigid all-movable elevator is fixed at the end of the aft-fuselage. In the resulting mathematical model, the pitching moment depends not only on the control surface position, but also on the rate and acceleration of the control surface motion. For compensation of the modeling uncertainties including the flexible dynamics, the L 1 adaptive control architecture is considered in this paper. It has a low-pass filter in the feedback loop allowing for arbitrarily fast adaptation with guaranteed robustness and transient performance for system's input and output signals. Simulation results demonstrate the benefits of the method.