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A quaternion-based attitude control system is developed for the X-33 in the ascent flight phase. A non-linear control law commands body-axis rotation rates that align the angular velocity vector with an Euler-axis defining the axis of rotation that takes the body-axis system into a desired-axis system. The magnitude of the commanded body rates are deter- mined by the magnitude of the rotation error. The commanded body rates form the input to a dynamic inversion-based adaptive/reconfigurable control law. The indirect adaptive control portion uses on-line system identification to estimate the current control effectiveness matrix to update a control allocation module. The control allocation runs in a null-space injection mode that excites and decorrelates the ef- fectors without degrading the vehicle response in or- der to enable on-line system identification. A direct adaptive control scheme uses the output of a neural network to compensate for dynamic inversion error. The overall system is designed to provide fault and damage tolerance for the X-33 on ascent. Prelimi- nary results are shown to demonstrate the feasibility of the approach.