Enabled is to lighten the load on a rider and to make the rider senses a turning state at the turning time of a transverse two-wheeled vehicle. A transverse acceleration (a) at a turn controlling time is detected to make a next inclination control in accordance with the magnitude of the acceleration. (a) In the case of an acceleration (a)≦a predetermined threshold (a0), the vehicle is left uninclined to prevent the vehicle body from being unnecessarily inclined and rocked against a small centrifugal force, thereby to improve the riding comfortableness. (b) In the case of the acceleration (a)>the threshold (a0), a riding portion is inclined such that the inclination angle θ1 may become the larger as the acceleration (a) becomes the higher. This can reduce the load on the rider against the centrifugal force. (c) As the acceleration (a) becomes the higher, the riding portion is so inclined the more as to increase the difference between the balanced inclination angle of the vehicle body and the inclination angle of the riding portion, so that the rider can bodily sense the increase/decrease of the centrifugal force.