An adaptive self-tuning control scheme is developed for end-point position control of flexible manipulators. The proposed scheme has three characteristics. First, it is based on a dynamic model of a flexible manipulator described in cartesian coordinates, which eliminates the burden and inaccuracy of translating a desired end-point trajectory to joint coordinates using inverse kinematic relations. Second, the effect of flexibility is included in the dynamic model by approximating flexible links with a number of rigid sublinks connected at fictitious joints. The relatively high stiffness of the fictitious joints is shown to result in a decomposition of the model into two subsystems operating at different rates. This allows for stabilization of the oscillatory modes associated with the flexible links by a fast feedback control in addition to a slower control for trajectory tracking. Third, the control is constructed from measurements of the end-point position and deformations of the flexible links, with the manipulator parameters required to form the control obtained using a recursive least-squares estimation algorithm, which is fast enough for on-line applications. Satisfactory results are obtained from digital simulation of a two-link flexible manipulator.