Heating catalysts during operation of internal combustion engines with direct injection

The method involves alternately producing lean combustion chamber fillings and rich fillings in the at least one combustion chamber, operating the engine (12) in a first mode with layered combustion chamber (16) fillings and a second mode with homogeneous combustion chamber fillings, with weak and rich combustion chamber fillings produced for the first and second modes respectively. An independent claim is also included for the following: (a) a controller for controlling the heating of catalyzers during operation of direct injection internal combustion engines.