A reducer with a double-clutch structure includes a source power input shaft and a power output shaft. A speed reduction mechanism includes a driving device and a driven device installed on the output shaft. A first clutch device is arranged on the output shaft and is driven by the driven device thereby driving the output shaft. A second clutch device is arranged on the output shaft and is meshed with the driven device to drive the output shaft. A clutch control device operates the first clutch device and the second clutch device simultaneously to move between the engaging position and the disengaging position. The first clutch device engages earlier than the second clutch device and disengages later than the second clutch device. When the clutch control device operates the second clutch device to move axially to an engaging position from a disengaging position, the first clutch device is axially pushed to the engaging position from the disengaging position by the second clutch device.