A vehicle having a suspended body (1), at least two wheels (2) each mounted on a wheel support. Each wheel support is mounted on a suspension device (5) comprising a suspension support (4) and means for guiding the wheel support relative to the suspension support. The suspension device allows a vertical displacement of the wheel support relative to the suspension support, the size of the displacement being sufficient to produce the vertical suspension movement required. At least one wheel is arranged transversely on one side of the body and at least one other wheel is arranged on the other side of the body. Each suspension support is connected to the body by a height variation mechanism (3, 7, 11, 12) which allows the relative height of the suspension support relative to the body (1) to be varied. Each height variation mechanism is actuated by height control means (15, 16, 17, 18). The vehicle has centralised control means (19) for the height control means, and the action of the height control means on each side of the body is coordinated so that on that side of the body, the relative height of each suspension support is varied simultaneously.