A diagnostic system in which the accuracy of the diagnosis of the deterioration state of a catalyst (40 in Fig. 1) in a catalytic converter (4) for cleaning the exhaust gas of an internal combustion engine (2) is enhanced without incurring a rise in cost. The temperature of the catalyst (40) is estimated using the operating-state signal (for example, the flow rate of intake air Q a or the width 120 of a fuel injection pulse) of the engine (2) by a diagnostic device (8). The conversion efficiency of the catalyst (40) calculated from the outputs of oxygen sensors (6a, 6b) is corrected using the estimated temperature by the diagnostic device (8). The deterioration state of the catalyst (40) is diagnosed on the basis of the corrected temperature by the diagnostic device (8).