When fluctuations in the speed of rotation of the drive pulley are transmitted to the driven pulley via the metal V-belt, the transmitted fluctuations become attenuated as friction force approaches a state of saturation. The research discussed in this paper focused on these fluctuations in the speed of rotation and developed an index for the slip state between the belt and the pulleys.The drive and driven pulleys were regarded as a one-dimensional vibrating system connected by elastic bodies, and changes in the state matrix of the system were focused on. It was determined that when all of the eigenvalues in this state matrix become real numbers, slip speed between the belt and the pulleys increases sharply. A method was proposed of estimating this behavior of the eigenvalues from changes in the speed of rotation of the drive and driven pulleys, and indexing the current slip state.Torque fluctuations reproducing the fluctuations produced by an engine were input to the drive pulley, and pulley thrust was gradually reduced in order to measure changes in slip speed. The friction drive limit found using the proposed method matched the point of increase in slip speed and the point of maximum power transmission efficiency as obtained from measurements, verifying the effectiveness of the method.Using the proposed method, it is possible to predict the friction drive limit, a parameter that is strongly affected by individual differences between parts and age-related changes, and this will contribute significantly to the optimization of pulley thrust.