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This paper presents a linear-adaptive design technique intended for the very severe parameter variation problems encountered in lifting re-entry vehicles and in flight control of modern aircraft. The technique is illustrated by means of a detailed application to the pitch axis stability augmentation system of the X-15. The problem is to obtain satisfactory vehicle response to command inputs and disturbances, despite the extremely large variations in vehicle parameters, which are encountered when Mach number varies from 6.0 to 0.2 and altitude varies from 160,000 ft to ground level. The given time domain specifications are translated into approximately equivalent frequency response restrictions, enabling the design details to be executed in the frequency domain. This results in the maximum economy in the gain and bandwidth of the system loop transmission. The design is verified by finding the time responses for some of the extreme conditions. The practicality of the design is discussed in terms of the gain and bandwidth demands on the compensating networks, the higher order airframe dynamics and the effects of any overdesign on the system saturation tendencies.