Abstract: An exhaust gas turbocharger consists of an exhaust gas turbine and a compressor mounted on a common shaft which can be driven by an electric motor controlled via a controller. The controller, which is designed as a computer, receives as control data the control input supplied to the controller of the internal combustion engine as the set value and actual performance values. The controller computes and supplies, from the received control data and from stored values, control signals by which, in the motor-operating mode of the electric motor, the internal combustion engine accelerates as quickly as possible at combustion air ratios optimal for low-smoke combustion and by which, in the generator-operating mode of the electric motor, a maximum of excess exhaust gas energy can be fed to an electric accumulator network as electrical energy via a static converter.