A lockup control apparatus for use with an automotive vehicle having an engine, an automatic transmission and a torque converter operable in a coast lockup mode having a lockup capacity to provide a controlled degree of mechanical connection between the engine and the automatic transmission when the vehicle is coasting. The apparatus employs a memory having a desired value for the lockup capacity stored therein. A first signal is produced when a slip rotation occurs in the torque converter and a second signal is produced when the coast lockup mode is released. The desired lockup capacity value is updated with a greater value in response to the first signal. A frequency at which either of the first and second signals occurs is measured. The desired lockup capacity value is updated with a smaller value when the measured frequency exceeds a reference value. The lockup capacity is controlled based on the desired lockup capacity value stored in the memory to retain the frequency of occurrence of the first signal in a predetermined range.