An exponentially stable direct adaptive control law for motion control of robot manipulators is presented. This control law utilizes the desired trajectory information instead of the actual manipulator joint signals for feedforward compensations and parameter adaptation. Computationally, it is extremely efficient. The exponential stability of the adaptive control algorithm is proven without requiring the persistent excitation condition and by fully considering the nonlinear dynamics of the manipulator in the analysis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>