Disclosed is a method, according to which the air fed to the combustion chambers of an internal combustion engine is pre-compressed by means of a boosting device, particularly an exhaust gas turbocharger. The valve overlap of the gas exchange valves of the internal combustion engine is adjusted by variably displacing the camshaft. The quantity of fuel to be injected, which is required for homogeneously operating the internal combustion engine, is determined and injected directly into the combustion chambers of the internal combustion engine, the total quantity of fuel to be injected being divided into two partial quantities. A first partial quantity is injected into the intake stroke while a second partial quantity is injected into the compression stroke. The ratio at which the two partial quantities are divided is defined according to the load range of the internal combustion engine.