An electric power steering apparatus for calculating a steering assist command value based on a steering torque and a velocity, generating a PWM signal based on said steering assist command value, PWM-controlling a three-phase brushless DC motor via a motor drive circuit comprised of switching elements, and assist-controlling a steering system that an electromagnetic type motor relay is inserted between said motor drive circuit and said three-phase brushless DC motor, characterized in that said electric power steering apparatus comprises: a temperature estimating section (120, 121, 122, 123, 123A, 124, 130, 130A, 131) that estimates a temperature of a relay spring portion or a relay coil portion of said electromagnetic type motor relay, a comparing section that compares an estimated temperature value that is estimated by said temperature estimating section (120, 121, 122, 123, 123A, 124, 130, 130A, 131) with a given temperature, a motor current control section that controls a motor current flowing in said electromagnetic type motor relay in accordance with a comparison result of said comparing section, and a substrate temperature sensor that detects a temperature of a substrate that is equipped with said electromagnetic type motor relay, wherein said substrate temperature is inputted into said temperature estimating section (124, 131), wherein said temperature estimating section (120, 121, 122, 123, 123A, 124, 130, 130A, 131) is a relay-spring-portion-temperature estimating section (120, 121, 122, 123, 124), said relay-spring-portion-temperature estimating section (120, 121, 122, 123, 124) comprises: an each-phase current accumulating section that accumulates detected each-phase current values of said three-phase brushless DC motor, a maximum value selecting section that selects a maximum value of accumulated values of said detected each-phase current values, a relay-spring-portion-temperature calculating section that calculates a relay-spring-portion-temperature based on a sum of said maximum value and a relay-coil-portion-temperature estimated-value, and an addition section that adds said substrate temperature and said relay-spring-portion-temperature and outputs said relay-spring-portion-temperature estimated-value. a temperature estimating section (120, 121, 122, 123, 123A, 124, 130, 130A, 131) that estimates a temperature of a relay spring portion or a relay coil portion of said electromagnetic type motor relay, a comparing section that compares an estimated temperature value that is estimated by said temperature estimating section (120, 121, 122, 123, 123A, 124, 130, 130A, 131) with a given temperature, a motor current control section that controls a motor current flowing in said electromagnetic type motor relay in accordance with a comparison result of said comparing section, and a substrate temperature sensor that detects a temperature of a substrate that is equipped with said electromagnetic type motor relay, wherein said substrate temperature is inputted into said temperature estimating section (124, 131), wherein said temperature estimating section (120, 121, 122, 123, 123A, 124, 130, 130A, 131) is a relay-spring-portion-temperature estimating section (120, 121, 122, 123, 124), said relay-spring-portion-temperature estimating section (120, 121, 122, 123, 124) comprises: an each-phase current accumulating section that accumulates detected each-phase current values of said three-phase brushless DC motor, a maximum value selecting section that selects a maximum value of accumulated values of said detected each-phase current values, a relay-spring-portion-temperature calculating section that calculates a relay-spring-portion-temperature based on a sum of said maximum value and a relay-coil-portion-temperature estimated-value, and an addition section that adds said substrate temperature and said relay-spring-portion-temperature and outputs said relay-spring-portion-temperature estimated-value. an each-phase current accumulating section that accumulates detected each-phase current values of said three-phase brushless DC motor, a maximum value selecting section that selects a maximum value of accumulated values of said detected each-phase current values, a relay-spring-portion-temperature calculating section that calculates a relay-spring-portion-temperature based on a sum of said maximum value and a relay-coil-portion-temperature estimated-value, and an addition section that adds said substrate temperature and said relay-spring-portion-temperature and outputs said relay-spring-portion-temperature estimated-value.