A driving force control apparatus is provided to prevent shocks from being generated during clutch engagement or release. The clutch is maintained in an engaged state and shocks are prevented from accompanying clutch release during creep travel when the target motor torque is equal to or less than a motor torque prescribed value but the average rear wheel speed, which is equivalent to the travel speed of the auto vehicle, is equal to or less than a low-speed prescribed value. In addition, the drive torque on the rear wheels from the electric motor is also brought to the same level as the creep torque on the front wheels from the internal combustion engine, backlash and other types of gaps between the rear axles of the electric motor are closed, and shocks are minimized or prevented during the subsequent transition to a four-wheel drive state.