This invention relates to a method and apparatus for controlling the air-fuel ratio demanded by a fuel controller in order to maintain optimum performance of a catalytic converter. The invention provides a controller for requesting an air fuel ratio according to a switching value derived from an estimated oxygen storage value of a catalyst, in which the controller is arranged to perform the following steps a) request a maximum ratio of air to fuel when the switching value is less than a first threshold; b) gradually decrease the requested air to fuel ratio from said maximum ratio; c) request a minimum ratio of air to fuel when the switching value is greater than a second threshold; and d) gradually increase the requested air to fuel ratio from said minimum ratio.