This note presents a novel adaptive compensation scheme for Coulomb friction in a servocontrol system. An adaptive observer for estimating the unknown Coulomb friction coefficient is also derived on the basis of the Lyapunov technique. In addition, a linearizing control Law is developed tea compensate for the friction force and obtain the tracking objective. The proposed adaptive compensation guarantees an exponential convergence for state errors and parameter error and the adaptive schemes in [1] and [3] guarantee only an asymptotic (or stable) convergence. Simulation results demonstrate the effectiveness of the proposed method for a single-mass servocontrol system.