This dissertation is concerned with the problem of slewing large flexible structures in space and simultaneously suppressing any vibrations. The equations of motion for a three-dimensional spacecraft undergoing large rigid-body maneuvers are derived. The elastic motions are assumed to remain in the linear range. A method of substructure synthesis is presented which spatially discretizes the equations of motion. A perturbation approach is used to solve the equations of motion. The zero-order equations describing the rigid-body maneuver are independent of the first-order vibration problem which includes small rigid-body motions. The vibration problem is described by linear nonself-adjoint equations with time-dependent coefficients. Minimum-time, single-axis rotational maneuvers are considered. The axis of rotation is not necessarily a principal axis. The optimal maneuver force distribution is proportional to the corresponding rigid-body modes with the mass acting as the control gain. The premaneuver eigenvectors are used as admissible vectors to reduce the degrees of freedom describing the vibration of the spacecraft during the maneuver. Natural control and uniform damping control are used to suppress the vibrations during the maneuver. Actuator dynamics cause a degradation of control performance. The inclusion of the actuator dynamics in the control formulation partially offsets this effect. The performance of these control techniques is adversely affected by actuator saturation but they remain effective. Numerical results are presented for a spacecraft in orbit and in an earth-based laboratory.