Manipulators with some flexible links are attractive because they avoid the severe control problems associated with the large inertia forces generated when the large-mass, rigid links in conventional robot manipulators move at high speed. In fact only two of the links within a typical six degrees of freedom revolute-geometry industrial robot cause significant inertia forces, and so only these two links need to be flexible. The development of a two-flexible-link system controller is therefore very relevant to larger manipulators, because it can be readily expanded by adding simple controllers for the other rigid links. Two alternative controllers are developed in this paper, a computed-torque controller and a quadratic optimal controller. Simulations confirm the superior performance of the latter.