In apparatus for controlling operation of a four-wheel drive vehicle having a prime mover (engine), drive wheels driven by the prime mover and free wheels, a VC (viscous coupling; torque transferring device) installed between the drive wheels and free wheels to transfer torque generated in response to a difference between inputted and outputted rotation thereof, output of the prime mover is decreased based on a desired rotational speed of the drive wheels driven by the prime mover when calculated difference between inputted and outputted rotation of the VC is equal to or greater than a predetermined value, thereby enabling to control the driving force effectively so as to achieve required vehicle driving performance.