A method for reducing the pollutant emissions in the exhaust gas in a start/catalytic converter heating phase of an internal combustion engine featuring externally supplied ignition and having at least one catalytic converter in an exhaust gas tract of the internal combustion engine, and for adapting a catalytic converter heating strategy to suitable state variables of the internal combustion engine and the catalytic converter as well as to the fuel quantity, the aging state and ambient conditions. The internal combustion engine is operated in a first phase of the start/catalytic converter heating phase using a lean air-fuel mixture in a range between a lambda value of 1.05 and at a lean misfire limit of the internal combustion engine that lies at a higher lambda value, and/or in a second phase of the start/catalytic converter heating phase, initially using a rich air-fuel mixture.