Robust control has a chattering problem since the control laws are discontinuous functions. To improve this, a boundary layer can be introduced; however the system then loses asymptotical stability and is only globally stable. An exponentially stable robust nonlinear control law for robot manipulators, based on Lyapunov stability theory, is presented. The robust control law is designed using a special Lyapunov function which includes both tracking errors and an exponentially convergent additional term, making the stability proof easy, and guarantees that the tracking errors decrease exponentially to zero. For bounded input disturbances, the control laws, with little modification, maintain satisfactory system performance. The results of a computer simulation for a 2-link manipulator are presented, demonstrating the benefits and robustness of the proposed algorithm.