In this paper we develop a robust adaptive control algorithm using a combination of H-infinity design and system identification. We derive frequency dependent bounds for the tolerated unmodeled dynamics and show that the approach gives a closed-loop system with bounded l(infinity) and l(2) gain when the model mismatch is small in the frequency range where the control gain is large. Our application focus is systems with structural flexibility. me present a parameter estimation algorithm that uses constrained least squares with prefiltering to overcome the problem of identifying lightly damped antiresonances (a common problem in identification of flexible systems). The estimation and control design are executed at a low frequency and only when parameter updating is needed. This allows us to apply computationally expensive control design and signal processing algorithms. It also eliminates many of the problems of earlier adaptive controllers (such as bursting, parameter drift, etc.) by turning off the estimator. We show results from the application of adaptive H-infinity control to a high-fidelity model of the Martin Marietta flexible beam testbed.