PURPOSE: To dispense with any installation of a cross-member mounting boss on top of a fork leg, thereby making any cutting work of the fork leg unnecessary and a tube usable for this leg by attaching a cross member to an upper part of the fork leg via a cross-member holder.

CONSTITUTION: A suspension system of a bicycle 10 consists of a pair of retractable suspension assemblies 21. Each suspension assembly 21 is composed of a slide tube 22 being clamped to a steering bracket 15, a tubular fork leg 23 being fitted in this slide tube 22 free of slide motion and holding a front-wheel hub, and an unillustrated damping force generator being interposed between these elements. In the above constitution, a cross-member holder 26 is fitted in a lower outer circumference in an upper end diametral expanding part of each fork leg 23. Then, each cross-member holder 26 is connected by a U-shaped cross member 27 with constant swing rigidity. With this constitution, such a requirement that the cross-member mounting boss is installed on top of each fork leg 23 is eliminated.