Method to operate an internal combustion engine with direct injection

In a process to operate a direct fuel-injected engine with exhaust gases discharging to a NOx storage catalytic converter, the motor is operated with a homogenous stoichiometric air/fuel ratio as a stratified charge engine, or in a homogenous lean-burn mode. In the process, a determination is made of the maximum permissible NOx raw mass and the maximum permissible exhaust gas mass flow determined at a momentary time point in relation to the NOx storage catalytic converter temperature. These measured values are compared with the predicted NOx raw mass flow and predicted exhaust gas flow for various lean-burn operating conditions. Based on this comparison a determination is made of whether the motor is operating under lean burn conditions or homogenous stoichiometric conditions.