In a vehicle having a pair of right and left front wheels and a pair of right and left rear wheels, when the front wheels are driven wheels, a differential limiting mechanism such as a multi-disc viscous clutch is arranged between axle members coupled to axles of the front wheels via universal joints, or when the rear wheels are driven wheels, the differential limiting mechanism is arranged between axles of the rear wheels. The differential limiting force of the differential limiting mechanism is controlled on the basis of various physical quantities (a steering angle .theta.h, a vehicle speed V, a brake hydraulic pressure P, a vertical acceleration G, and a road-surface .mu.) associated with the traveling state of the vehicle detected by sensors. Therefore, there can be provided a driven wheel differential limiting apparatus for a vehicle, which has high reliability and durability since the differential limiting force is controlled via, e.g., the viscous force of a fluid, and which can assure quick-turn traveling performance at a low vehicle speed, and can improve straight traveling stability in a high-speed traveling state since the degree of differential limiting is varied in correspondence with the traveling state of the vehicle.