The riding height of the motorcycle is adjustable via a movable support (28) for the rear wheel mounting. For a simple control the height is reduced at fast road speeds and is at maximum during starting. Two speed limits are provided by the control to set the start of height increase or lowering. The riding height control takes into account the dynamic changes in the motorcycle speed, i.e. braking and acceleration as well as the dynamic response of the adjustment and that of the control system to generate optimum control signals for the riding height control for maximum comfort and stability.