A catalyst degradation determining method includes the steps of: controlling an upstream-of-catalyst air-fuel ratio occurring upstream of a first catalyst to an air-fuel ratio that is rich of a stoichiometric air-fuel ratio so that first and second catalysts store oxygen up to a maximum storage amount of oxygen. The method then includes the steps of controlling the upstream-of-catalyst air-fuel ratio to a first lean air-fuel ratio until an output of a downstream-of-first-catalyst sensor indicates a lean air-fuel ratio, and then to a second lean air-fuel ratio and that has a value that is determined in accordance with an oxidizing-reducing capability index value, until a time point when an output of a downstream-of-second-catalyst air-fuel ratio sensor indicates an air-fuel ratio that is lean.