A traction control system (TCS) for two-wheel-drive vehicles can conveniently be realized by means of slip control. Such a TCS is modified in this paper in order to be applicable to four-wheel-drive vehicles and ABS, where slip information is not readily available. A reference vehicle model is used to estimate the vehicle velocity. The reference model is excited by a saw-tooth signal to adapt the slip for maximum tire traction performance. The model-based TCS is made robust to vehicle modeling errors by extending it with (i) superimposed loop of tire static curve gradient control or (ii) a robust switching controller based on a bi-directional saw-tooth excitation signal. The proposed traction control strategies are verified by experiments and computer simulations.