a control apparatus for rapidly warming up a catalyst disposed within an exhaust pipe connected to an internal combustion engine . the control apparatus first determines a fuel injection amount and an ignition timing of the engine on the basis of an engine operating condition such as an intake air pressure of the engine and a rotational speed of the engine . the control apparatus is also responsive to temperature information of the catalyst for adjusting the fuel injection amount and the ignition timing in accordance with the catalyst temperature information . when the catalyst temperature does not reach the effective emission - purifying temperature , the control apparatus alternately adjusts the fuel injection amount to a rich amount and a lean amount and further intermittently retards the ignition timing . this injection and ignition control operation allows acceleration of the warming - up of the catalyst to suppress the deterioration of the emissions from the engine .