Abstract: Dual oxygen sensors before and after the exhaust catalytic converter of a motor vehicle combined with a specialized algorithm to substantially continuously compare the real time electric output of the oxygen sensors and, in response to the comparison, output an indication of the activity of the catalyst and failure of the catalyst. The algorithm in substantially real time "monitors" the continuously changing oxygen content of the before and after catalyst exhaust stream and through a phase comparison or an integration process in the preferred embodiment makes the proper comparison for determination of catalyst acceptability or failure. With a microcomputer equipped motor vehicle the algorithm is suitable for on-board continuous monitoring of the exhaust catalyst for indication to the vehicle operator when catalyst failure occurs. Failure can be total catalyst failure or partial failure to a degree where Federal exhaust emissions regulations are no longer met.