A transmission box (3) for a wheeled machine includes a motor input shaft (4) driving a drive wheel (8) to actuate at least one drive shaft (9A, 9B) of at least one wheel (2A, 2B) of the machine (1). A clutch mechanism (13) is disposed between the drive wheel (8) and a drive shaft (9A, 9B) and is actuated by driving in rotation the drive wheel (8) and deactuated by driving in rotation the drive shaft (9A, 9B) when the motor input shaft (4) is stopped or when the speed of rotation of the drive shaft (9A, 9B) is greater than the speed of rotation of the drive wheel (8). The box (3) contains two clutch mechanisms (13), each coacting with one drive shaft (9A, 9B) to permit the free wheeling of one and/or the other of a pair of wheels (2A, 2B).