To provide a transmission device with a plurality of clutches capable of instantaneously and properly controlling the driving force of driving wheels not to slip at sudden start or start or travel on a rough road and superior in economic efficiency.

The transmission device with the plurality of clutches comprises a first clutch for on-off operation of driving force transmission to a first input shaft having a driving gear meshing with a driven gear of the output shaft of a transmission to be driven by a driving force generating means, a second clutch independent from the first clutch for on-off operation of driving force transmission to a second input shaft having a driving gear meshing with a driven gear of the output shaft of the transmission to be driven by the driving force generating means, a driving force detecting means for detecting driving force generated by the driving force generating means, a slip detecting means for detecting the physical quantity regarding the slip of the driving wheels, and a second clutch control means for inputting the detection results of the driving force and the physical quantity regarding the slip and controlling the joint rate of the second clutch in the state that the first clutch is joined thereto.