An auxiliary driving system is provided to ensure that a vehicle equipped with an automatic transmission can be moved or permitted to travel without use of the driving force of the vehicle engine in the event of an emergency. The main driving wheels are normally driven through an engine and an automatic transmission and a pair of auxiliary driving wheels are driven by motors. In a usual state, the motors are used to generate an auxiliary driving force or a creep force in the vehicle. However, if the vehicle engine is stopped due to engine trouble or failure, the motors can be driven based on the amount of accelerator pedal depressed to rotate the auxiliary driving wheels and thereby permit the vehicle to travel. Thus, movement of the vehicle can be easily accommodated in the event of an emergency such as when the vehicle engine has failed.