Abstract: So that sufficient combustion air is available in all the cylinders of a diesel internal combustion engine both under part load and in transient operating states, oxygen-containing gas or additional gas or compressed air from a gas distributor is additionally supplied under pressure to the combustion space of the cylinder, even after the diesel internal engine has been started, through at least one separate additional-gas inlet by means of at least one separate additional-gas valve (V1a). The supply of this additional gas can commence after closing of an air inlet valve (VE) or of an air outlet valve (VA) of the diesel internal combustion engine. The method is suitable for both 4-stroke and 2-stroke diesel internal combustion engines.