The present invention relates firstly to a method for operating a compressor powered by an internal combustion engine for compressing air. Furthermore, the invention relates to a compressor, which is suitable for executing the method according to the invention. A first turbocharger for supplying pre-compressed air to the internal combustion engine is disposed in an exhaust flow of the internal combustion engine. Furthermore, a second turbocharger for pre-compression of the air to be compressed by the compressor is disposed in the exhaust flow of the internal combustion engine. The method according to the invention first comprises a step in which a monitoring of a pressure of the pre-compressed air generated by the first turbocharger occurs during an operating state of the compressor. In a further step of the method, a termination of the operating state occurs as soon as the monitored pressure falls below a previously determined value.