To provide the differential for a vehicle, which is simple in structure with no frictional clutch structure provided.

A case 3O of a differential is provided with a center wall 40 dividing the inner part of the case into a first fluid chamber 41 and a second chamber 51. The end parts of axle shafts 22 and 24 are extended to the insides of the respective fluid chambers. The respective fluid chambers are filled with rheological fluid. Electromagnetic coils 44, 45, 54 and 55 are disposed in the respective fluid chamber or while being adjacent to the respective fluid chambers. An electronic control device 61 is provided so as to allow current to be fed to each electromagnetic coil in response to the detectable maneuvering conditions of a vehicle, for example, the revolving speed of each axle shaft and the magnitude of torque. Magnetic field strength to be applied to rheological fluid filled in the fluid chambers can be changed by changing the amperage of current to be fed to each electromagnetic coil. Therefore, Resistance against the flow movement or shearing of rheological fluid exerting influence on the magnitude of torque to be transmitted to each axle shaft, can thereby be changed in response to the maneuvering condition of the vehicle.