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The problem of controlling flexible space structures in the presence of significant uncertainties using only position measurements is considered. Adaptive controllers, which are capable of controlling partially known dynamical systems and delivering good performance by providing a time-varying compensation on-line, are desirable for such system. We present an adaptive controller which can globally stabilize a class of flexible structures. This controller is applicable whether position measurements, rate measurements, or combinations thereof are available, as well as for colocated and noncolocated actuator-sensor pairs that are sufficiently close. The improvement in performance generated using such controllers is demonstrated using two practical structural system.