In a method for cold-running or warm-up operation of a spark-ignition, direct-injection 4-stroke internal combustion engine having an exhaust gas catalytic converter, wherein fuel is injected into the cylinders of the internal combustion engine by means of injectors and is externally ignited by means of spark plugs, in an intake stroke fuel injection a lean, combustible but non-ignitable lean mixture is produced in the cylinders, in a compression stroke fuel injection following the intake stroke injection, by a compression stroke fuel injection, a combustible and ignitable fuel/air mixture is formed in the combustible but non-ignitable lean mixture in the cylinders and, subsequently, in a stratified fuel injection which is close in timing to an ignition time, a rich fuel/air mixture is locally formed in the region of the spark plug and is then ignited by the spark plug so as to provide for rapid heat up of the cold exhaust gas catalytic converter with reliable combustion and smooth engine operation.