A slip control apparatus for a fluid-operated lock-up clutch in a power transmitting system of a motor vehicle, wherein the amount of slip of the lock-up clutch is controlled such that the actual slip speed of the clutch coincides with a target value. The apparatus includes a device for establishing a restricted slip control mode if the vehicle running condition upon detection of a judder of the clutch is in a first area in which the clutch is likely to experience the judder. In the restricted slip control mode, the slip control of the clutch is inhibited while the vehicle running condition is in the first area, but is permitted while the vehicle running condition is in a second area in which the clutch is unlikely to experience the judder. The first and second areas of the vehicle running conditions are defined by parameters such as engine load or throttle valve opening and temperature of an oil used for operating the clutch.