Abstract: The invention relates to a vehicle provided with a per se known supporting system (2) on a support (3) of its path and provided with at least one auxiliary wheel (1). The wheel (1) is joined to the frame (2) of the vehicle by means of a support (22a) for its axis of rotation and of a hinged linkage system (23, 24) of said support to the frame enabling the constant maintaining of the wheel in contact with a supporting surface (3) with known friction which is parallel with the path A of the vehicle and from which the frame (2) is held at a distance D which remains substantially fixed by a high resilient rigidity arrangement (12), said connections system being such that when the wheel is subjected to a force F contained in said supporting surface and being exerted at the point of contact C of the wheel (1) with the surface (6) said force produces a reaction force Q of the high resilient rigidity arrangement proportional to F tending to apply the wheel (1) against the surface (3).