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.