In a system for cleaning tubes of heat exchangers flown through by a fluid medium, in particular crude oil, having a temperature in excess of 120 C., wherein, for cleaning a tube, deposits such as dirt particles or the like adhering to its inner wall are detached by cleansing off and carried out of the tube, for cleaning the inner wall of the heat exchanger tubes during the operation of the heat exchanger, it is provided that cleaning bodies withstanding high temperatures (in excess of 120 C.) as well as withstanding aggressive fluid media such as crude oil and having outer dimensions when cleaning equal to the inner diameter of the tube to be cleaned and having an outer contact surface suitable for cleansing off deposits from an inner wall of a tube, pass through the tube due to the pressure of the fluid medium and are pressed to the inner wall of the tube by a contact pressure, and that, during the passage of the cleaning bodies, deposits adhering to the inner wall of the tube are caught and detached by the contact surface of the cleaning bodies and carried along by the fluid medium and/or the cleaning body and carried out of the tube.