A system and method for estimating surface coefficient of friction in a vehicle system. The method includes providing a kinematics relationship between vehicle yaw-rate, vehicle speed, vehicle steering angle and vehicle front and rear axle side-slip angles that is accurate for all surface coefficient of frictions on which the vehicle may be traveling. The method defines a nonlinear function for the front and rear axle side-slip angles relating to front and rear lateral forces and coefficient of friction, and uses the nonlinear function in the kinematics relationship. The method also provides a linear relationship of the front and rear axle side-slip angles and the front and rear lateral forces using the kinematics relationship. The method determines that the vehicle dynamics have become nonlinear using the linear relationship and then estimates the surface coefficient of friction when the vehicle dynamics are nonlinear.