An electric power steering apparatus drives a motor to generate a steering assist force according to a steering torque and includes an output circuit for supplying the motor with electric power from at least one of a battery and an auxiliary power supply. The electric power steering apparatus has a control circuit which at or after detection of a breakdown of the battery, determines a length of time to the end of steering assist (decreasing time t1) based on the amount of energy stored in the auxiliary power supplies and which takes the determined length of time to perform output decreasing control to gradually decrease the upper limit of power supplied for the steering assist to practically zero according to a constant gradient. Thus is provided an electric power steering apparatus which is adapted to prevent a sudden fall of the steering assist force in the event of a battery breakdown while effectively utilizing the available stored energy.
