The Generic Hypersonic Aerodynamics Model Example (GHAME) provides a practical benchmark for evaluating advanced control strategies for hypersonic vehicles. Its nonlinear dynamics and strong aero-propulsive coupling make it suitable for assessing nonlinear control methods. Although GHAME is the only publicly available hypersonic model derived from real flight data, Nonlinear Dynamic Inversion (NDI) has not previously been applied to it. This study develops a hierarchical control architecture based on time scale separation, combining NDI for attitude and position control with Incremental Nonlinear Dynamic Inversion (INDI) for angular-rate and velocity control. The implementation is carried out in MATLAB and Simulink, and the controller is tested under model uncertainty, atmospheric disturbances, and additionally tested under synchronized and desynchronized measurement time delays. The controller achieves accurate tracking when no delay is present. Under desynchronized delays, performance degrades rapidly and similarly in both axes. Under synchronized delays, degradation is more gradual: the lateral dynamics lose stability at roughly half of the allowable delay margin, whereas the longitudinal dynamics remain stable until the full margin is reached. This behavior reflects the very short natural time constants of the lateral subsystem in slender hypersonic configurations, which reduce the effectiveness of the assumed time scale separation. Overall, the study provides the first NDI application to the GHAME model and demonstrates that an NDI–INDI architecture can remain effective under uncertainty, disturbances, and realistic time delays when synchronization is maintained, although its application must be approached with caution due to the heightened sensitivity of the lateral dynamics. The findings naturally pave the way for future investigations, including flight envelope protection strategies, and integration with guidance and trajectory optimization methods for hypersonic missions.