In this article, an adaptive multiple-model-based fault-tolerant controller is developed for nonminimum phase air-breathing hypersonic vehicles (HSVs) in the presence of parametric uncertainties, elevator faults, input saturations, and time-varying error constraints. Compared with the existing works, the elevator-to-lift couplings are taken into account, which makes the HSV longitudinal models exhibit unstable internal-dynamics that impedes the applicability of common nonlinear control methods for control design. In order to solve this problem, a two-layer cascade control strategy is proposed in which the external inputs control the external states and the external state deviations control the internal states: 1) A multiple-model linear quadratic control strategy, based on gap metric, is proposed to guarantee the stability of the internal dynamics; 2) a fault-tolerant control scheme, based on tan-barrier Lyapunov functions, is developed by using a low-pass filter and an auxiliary system in conjunction with adaptive backstepping design. In the control law, the uncertain parameters are replaced by their estimates updated by adaptive laws. Additionally, the stability of the whole system is rigidly proved through standard Lyapunov approach, while the other states and signals in the closed-loop system are guaranteed to be bounded. Simulation results are provided to illustrate the effectiveness of the proposed adaptive multiple-model-based fault-tolerant controller.