For the direct re-entry in the CAI operating mode following a pull fuel cut off phase the CAI specific valve lift is maintained during its pull fuel cut off phase. Upon a request signal for the CAI re-entry after the closing time of the particular cylinder, an advance fuel injection quantity is injected in the combustion chamber and externally ignited and combusted in the following CAI interim compression phase of the exhaust stroke, as a result of which hot exhaust gas is formed in the combustion chamber, fresh air is drawn into the combustion chamber during the following intake stroke, a main fuel injection quantity is injected in a main compression phase during the following compression stroke, and the exhaust gas content brought about from the earlier auxiliary fuel injection, is mixed with the air-fuel mixture newly introduced for the main ignition to form a self-ignitable, homogenous fresh air-exhaust gas-fuel mixture.