In a four wheel drive power transmission system for a vehicle, a power distribution device receives rotational power from an engine (1) and provides rotational power to the combination of the front wheels and also to the combination of the rear wheels, and is controllable either to provide differential action between the front wheels combination and the rear wheels combination, or for this differential action to be at least partially inhibited by torque transmission. This slippage control device (45) includes: a subsystem which estimates the torque (49) being input to the power distribution device for four wheel drive from the transmission mechanism; and a subsystem which provides differential action inhibition of the power distribution device according to the thus estimated value of the torque being input to it from the transmission mechanism. The method of operation of this device is also described.