This paper is focused on the design of a control strategy for the path tracking of off-road mobile robots acting at high speed. In order to achieve high accuracy in such a context, uncertain and fast dynamics have to be explicitly taken into account. Since these phenomena (grip conditions, delays due to inertial and low-level control properties) are hardly measurable directly, the proposed approach relies on predictive and observer-based adaptive control techniques. In particular, the adaptive part is based on an observer loop, taking advantage of both kinematic and dynamic vehicle models. This multi-model based adaptive approach permits to adapt on-line the grip conditions (represented by cornering stiffnesses), enabling highly reactive sideslip angles observation and then accurate path tracking. The relevance of this approach is investigated through full scale experiments.