The Extended Proximate Time-Optimal Servo (XPTOS) developed in [8] is analyzed for stability using new techniques. The XPTOS system operates in closed loop, and blends in its structure the characteristics of a time-optimal control law and the fine tracking properties of a properly tuned linear regulator. This study is addressed to the (idealized) case of flexible structures that contain a single or dominant structural mode. Simulation results demonstrate the performance of the XPTOS, and delineate its range of applicability.