An air/fuel ratio control apparatus an internal combustion engine, and an engine control unit are provided for conducting perturbation control to maintain a satisfactory exhaust gas purification percentage irrespective of whether or not a catalyst is deteriorated. The air/fuel ratio control apparatus for an internal combustion engine includes an ECU, and a LAF sensor and an O2 sensor disposed at locations upstream and downstream of a first catalyst, respectively, in an exhaust pipe. The ECU sets a target air/fuel ratio for converging the output of the O2 sensor to a predetermined target value such that it fluctuates over a predetermined amplitude at a predetermined frequency higher when the output of the O2 sensor remains near a predetermined target value than when it is not near the predetermined target value. The ECU also controls an air/fuel ratio to match the output of the LAF sensor with the target air/fuel ratio KCMD.