In order to operate an internal combustion engine with a turbocharger, a boost pressure prevailing downstream of a compressor (42) of the exhaust gas turbocharger and upstream of a cylinder intake port of the internal combustion engine is regulated to a predefined desired boost pressure value (PUT_SP). An actuation signal portion (DELTA_PWM_WG) of a controller for regulating the boost pressure to a desired boost pressure value (PUT_SP) is determined. A change in the turbocharger speed (DELTA_N_TCHA) associated with the actuation signal portion (DELTA_PWM_WG) of the controller is determined in accordance with the actuation signal portion (DELTA_PWM_WG) of the controller and an operating point of the internal combustion engine. A turbocharger speed limit (N_TCHA_MAX) is determined in accordance with the determined change in the turbocharger speed (DELTA_PWM_WG).