A catalyst deterioration-determining system determines deterioration of a catalyst arranged in the exhaust passage of an internal combustion engine. An ECU is responsive to an output from an O.sub.2 sensor arranged upstream of the catalyst or outputs from O.sub.2 sensors arranged upstream and downstream of the catalyst for controlling the air-fuel ratio of a mixture supplied to the engine by means of an air-fuel ratio correction value (first air-fuel ratio control). When the engine is in a predetermined operating condition, the system effects changeover from the first air-fuel ratio control to a second air-fuel ratio control which is responsive to the output from the downstream O.sub.2 sensor for controlling the air-fuel ratio of the mixture by means of the air-fuel ratio correction value. After the changeover has been effected, a time period is measured which elapses from the time the second air-fuel ratio control causes a change in the air-fuel ratio correction value from a richer side to a leaner side or vice versa with respect to a stoichiometric air-fuel ratio to the time the output from the downstream O.sub.2 sensor is inverted from the richer side to the leaner side or vice versa with respect to the stoichiometric air-fuel ratio. It is determined that the catalyst is deteriorated, when the measured time period is shorter than the predetermined time period.