A method, and an apparatus for carrying out the method, for purifying exhaust gases from internal combustion engines is provided. The engines having a catalyzer system which includes a first catalyzer and at least one second catalyzer, arranged downstream of the first catalyzer, for the conversion of HC, CO and NO.sub.x exhaust gas constituents. Exhaust gases flow through both catalyzers during the entire operating period of the engine. The first catalyzer is suitable for at least the catalytic conversion of HC and CO exhaust gas constituents. In a first step of the method, the first catalyzer is operated over-stoichiometrically during the cold starting phase in order to reduce the HC and CO emissions and, in a second step of the method with .lambda.-controlled stoichiometric exhaust gas composition, the catalytic conversion of the exhaust gas is at least largely de-activated and in the first catalyzer takes place in the second catalyzer. Substantially better endurance of the first catalyzer is attained for the same good reduction in the exhaust gas pollutants.