Special conveying systems are used within a production plant in order to transport agricultural products such as, in particular, eggs. Here, a conveyor chain 14 having a multiplicity of rods 42 which are connected to one another via chain links 44 is transported in individual conveying segments 12 of the conveyor 10. Lying on the conveyor chain 14, the products, in particular the eggs, are transported. Deposits of contaminants unavoidably occur during operation, such as, in particular, as a result of litter or feathers. Contaminants which adhere only loosely can be removed in a simple way, for example, by suitable strippers.It is the object of the invention to also eliminate contaminants which adhere firmly and as far as possible to also minimize the number of microorganisms. This is achieved by the use of an ultrasonic cleaning bath 30, into which a section of the conveyor 10 is dipped with the aid of a deflecting unit 16. During the normal revolution of the conveyor chain 14, cleaning of the conveyor chain 14 can thus be carried out even during running operation of the conveying system by means of ultrasound and suitable cleaning agent.