In an abnormality diagnostic device and an abnormality diagnostic device for an air-fuel ratio sensor that detects the air-fuel ratio of exhaust gas of an internal combustion engine, a system extending from a fuel injection valve to the air-fuel ratio sensor is model by a first order response delay, and a parameter in the first order response delay is identified based on an input air-fuel ratio that is given to the air-fuel ratio sensor and an output air-fuel ratio that is output from the air-fuel ratio sensor. Then, the presence/absence of abnormality regarding a predetermined characteristic of the air-fuel ratio sensor is determined based on the parameter identified. Thus, abnormality is diagnosed regarding individual characteristics of the air-fuel ratio sensor.