An apparatus including a slip control device for controlling an amount of slip of a lock-up clutch disposed between pump and turbine impellers in a power transmission system of a motor vehicle, a slip-parameter monitoring device for detecting the actual slip speed of the lock-up clutch or a control error between actual and target slip speeds of the lock-up clutch, a summing device for obtaining a sum of values of the actual slip speed or control error detected by the slip-parameter monitoring device for a predetermined period of time, and a defect detecting device for determining the presence or absence of a defect in slip control of the lock-up clutch by the slip control device, on the basis of the sum as compared with a predetermined reference.