Abstract: Disclosed is a two-way-driven 3-speed free wheel which provides a multi-gear-changing mechanism for use with various kinds of pedal cycles. The disclosed device has four kinds of catches: pawl, hook-pawl, backward pawl and forward pawl. The backward and forward pawls respectively are hinged on the opposed sides of a sprocket wheel by small spindles mounted on the opposed sides of the sprocket wheel. On one side of the sprocket wheel are the backward pawls and an outer ring; on the other side are forward pawls, a ratchet cone and a bearing collar. Between the outer ring and a central gear are two or more planet pinions. As compared with prior art structures, this invention has the following advantages: the structure is simple, the cost is lower, and it is facile to operate and to change speed. Also disclosed are one-way-driven 2-speed free wheels and two-way-driven 2-speed free wheels, using two or three kinds of catches, of the above-described four kinds of catches.