An anti-lock braking system includes a friction torque gradient estimating unit for estimating, from a small number of parameters, the gradient of friction torque with respect to a slip speed, and controls a braking force acting on wheels on the basis of the friction torque gradient estimated by the friction torque gradient estimating unit. The friction torque gradient estimating unit may employ several types of estimating methods; e.g., a method of estimating the gradient of friction torque from only time-series data concerning a wheel speed; a method of estimating the friction torque gradient from time-series data concerning wheel deceleration as well as from braking torque or time-series data concerning physical quantities associated with the braking torque; or a method of estimating the friction torque gradient from micro-gains which are obtained when brake pressure is excited in a very small amount at the resonance frequency of a vibration system comprising a vehicle, wheels, and a road surface and which represent the characteristics of the vibration system. Further, there is also disclosed a method of determining, from the thus-estimated friction torque gradient, the limit of the characteristics of friction torque developed between the wheels and the road surface.