1. A turbocharger with a device for detecting a malfunction of the turbocharger, in particular a malfunction of at least one bearing of the turbocharger, wherein a) the device for detecting a malfunction of the turbocharger comprises a memory device in which the desired rotational speed curves of an intact turbocharger are stored, b) the device for detecting a malfunction of the turbocharger comprises a comparing device in which the detected actual rotational speed curve of the turbocharger is compared to a corresponding desired rotational speed curve of an intact turbocharger, c) the turbocharger comprises a measuring device for determining an actual rotational speed curve of the turbocharger, and wherein d) the device for detecting a malfunction of the turbocharger issuing an error message if the comparing device detects that the actual rotating speed reaches a limit rotational speed within a period of time and the period of time in this process lies outside a tolerance range for a desired period of time, within which an intact turbocharger reaches the limit rotational speed.