A gear-shifting apparatus is provided which easily returns a derailed chain to engagement with a tension and/or guide pulley when the chain comes off the respective pulley due to a gear-shifting operation, and enables a gear-shifting operation to be performed when a gear-shifting is halted or is rotating backward. A derailer includes an arm which supports a tension pulley and a pulley support member which supports a guide pulley. The arm is provided with engagement recovery-guiding parts for causing respectively derailed parts of a chain, which are derailed from the orbital plane of the tension pulley, to engage with the tension pulley. The pulley support member is provided with a first extending part and a second extending part for the purpose of causing derailed parts of a chain, which has been derailed from the orbital plane of the guide pulley, to engage with the guide pulley.