The invention concerns a two-wheel vehicle equipped with lateral stabilising wheels (18) whereof the passage from a retracted position into an active state, and inversely, is automatically carried out when a predetermined speed threshold is exceeded. Moreover, each stabilising wheel (18) is provided with a damper jack (52) whereof the rigidity decreases with speed, when the wheels are in active state. An inclination sensor (23) commands the vehicle to be upright when the stabilising wheels are in active state. Thus a gradual transition is achieved between a two-wheel type vehicle behaviour and a four-wheel type vehicle behaviour, thereby making the most of the advantages particular to the two types of vehicles, without requiring any particular training for the driver.
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