PURPOSE: To make a follow-up movement of front wheel well operated for the travelling surface, by providing a swingable front wheel support substance in the bottom end part of a steering shaft.

CONSTITUTION: A steering shaft 8, with a caster angle provided, is rotatably supported by a body 1, and rotated interlocking to a handle 8'. In the bottom end part of the steering shaft 8, is provided an axle 9 extended longitudinally of the body 1. To this axle 9, is swingably installed a front wheel support substance 10 with its axle core being the center. A balloon tire 12, 13, if mounted to the front two-wheel suspension system of such constitution, being freely swingable with the axle 9 being the center, is not made floating from the travelling surface even when travelling on a road of rugged surface and also when turning to right and left, with a follow-up motion well operated on the travelling surface. And if provided a stopper substance in the side of the steering shaft 8 for adjusting a swinging angle with the axle 9 being the center, a shock, according to a control of the swinging motion, can be prevented.