The present invention provides a chainless multi-stage derailleur device free from stuck-chain, de-railed chain and other issues for various bicycles. The technological means includes: a derailleur device on the sprocket shaft of bicycle rear wheel; and a driving device connected with derailleur device; it is characterized: the derailleur device has a driven member on sprocket shaft with the first elongated hole at the edge; a drive member located on one side of the driven member for rotation; and a control device engaging with the drive member to control drive member the decrease or increase of the moment of inertia. In this way, the speed of the bicycle will change due to the increase or decrease of rotation momentum when the rider pedals the bicycle with the same power. Therefore, by increasing the screw length of the derailleur device, the multi-stage gear changes of 20, 30, and 40 can be realized. It overcomes the barrier of transmission by chain and solves the structure and weight issues of ratchet.