In a system for cleaning tubes of tube-bundle type heat exchangers including a plurality of tubes (5) arranged in parallel between two chambers (10a, 10b) and flown through by a fluid medium, in particular crude oil, at a temperature above 120.degree. C., wherein, for cleaning the tubes (5), deposits on their inner walls, such as coking, dirt particles or the like, are detached by cleaning bodies passing through the tubes (5), and carried out of the tubes (5), for cleaning the inner wall of the plurality of tubes (5) of the heat exchanger during the operation of the heat exchanger (10), it is provided that the cleaning bodies (1a 1h) are formed in such a way that they are resistant to high temperatures (above 120.degree. C.) and withstand aggressive fluid media such as crude oil and are freely transported in the flowing fluid medium, in particular with large flow-through diameters, such as in the chambers (10a, 10b) of the heat exchanger (10) and sink or rise in the stagnant fluid medium, and have an outer contact surface suitable for removing deposits from a tube inner wall, pass through the tubes (5) due to the pressure of the fluid medium, and have their contact surfaces forced against the tube inner wall by contact pressure.