This paper addresses the problem of controlling a two-flexible-link manipulator. The idea of industrial manipulators having some lightweight, flexible links is attractive if high-speed motion is required in manufacturing operations 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 the commonest form of industrial robot, the six-degrees-of-freedom (6DOF) revolute-geometry type, only two of the links (the upper and lower arm) are subjected to significant inertia forces and therefore only these two links need to be lightweight and flexible. A two-flexible-link system controller is an appropriate starting point for dealing with such a 6DOF robot, because this can be readily expanded by adding simple controllers for the other rigid links. A modified computed torque algorithm is shown by simulation with MATLAB to control satisfactorily the oscillatory tendency of the two-flexible-link system.