The time optimal slewing problem for flexible spacecraft is considered. We study single-axis rotational maneuvers for a simple flexible system, consisting of a rigid hub with an elastic appendage. The equations of motions are derived by Hamilton’s Principle, and a discrete nonlinear model is obtained by the assumed modes method. The problem is first solved in a discrete linearized space by parameter optimization. Optimality is verified by Pontryagin’s Maximum Principle. The linear solutions are then used to obtain time optimal solutions for the non-linear problem by a multiple-shooting algorithm. Although this approach is applicable to arbitrary boundary conditions, this work is confined, almost exclusively, to rest-to-rest maneuvers. These maneuvers are shown to possess some interesting symmetric and asymptotic properties. The problem is further analyzed in infinite-dimensional space, and the convergence of the finite-dimensional approximations is studied. Finally, a soft version of the time optimal slewing problem is considered, where the control is bounded only by a penalty term in the cost functional. A perturbation technique is applied to further simplify this problem. / Ph. D.