An exhaust turbocharger for an internal combustion engine has a main compressor for compressing the fresh air supplied to the engine, an additional compressor for compressing combustion gases to be recycled to the engine, and a turbine that can be driven by the exhaust gases from the engine and which serves to drive the main compressor and the additional compressor. The turbine has an adjustable geometry which facilitates optimization of engine operation regarding pollutant emissions, fuel consumption, and performance.