In this paper incremental nonlinear dynamic inversion, a sensor based approximate form of feedback linearization with favorable robustness properties, is applied to the traction control and stability augmentation problem of a Le Mans Prototype 1 race car. A cascaded side-slip and yaw-rate envelope protection system is developed in combination with a model following yaw-rate controller which acts inside the safe envelope. The vehicle is controlled through two limited slip differentials featured in the front and rear of the vehicle. A method is presented to account for load tranfer effects in the calculation of the limited control effectiveness associated the actuators . Simulations with a high-fidelity vehicle model demonstrate that the control system is robust against parameter uncertainties and is able to effectively keep the vehicle within the bounds of the safe envelope.