An observer for estimating the vector of Coulomb friction force coefficients in a multimass system is presented. The vector is assumed to be a linear combination of sgn(·) functions of relative velocities of the contacting masses. Two different nonlinear observers are proposed to estimate the friction coefficients when the velocities of the masses can be measured. When only the positions of the masses can be measured, an additional (reduced-order observer) is used to estimate the velocities of the masses. Excellent performance of the proposed system in the presence of white noise, is demonstrated by simulation.