Driving force controlling apparatus and method for four-wheel drive vehicle

In driving force controlling apparatus and method for a four-wheel drive vehicle, a command is outputted to a front-and-rear wheel driving force distribution control system to reduce a clutch engagement force of a clutch, such as a frictional clutch, when a subtraction value of a detected value of a clutch transmission torque from that of a clutch input torque (Tinp - Tr) is smaller than a predetermined value ( delta ) and detected wheel velocities of both of left and right road wheels of the vehicle are substantially equal to each other (Vw1 +/- alpha = Vw2 and Vw3 +/- alpha = Vw4).