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To timely detect failed fuel elements, a reactor plant should be equipped with a fuel cladding tightness monitoring system (FCTMS). In reactors using a heavy liquid-metal coolant (HLMC), the most efficient way to monitor the fuel cladding tightness is by detecting gaseous fission products (GFP). The article describes the basic principles of constructing a FCTMS in liquid-metal-cooled reactors based on the detection of fission products and delayed neutrons. It is noted that in a reactor plant using a HLMC the fuel cladding tightness is the most efficiently monitored by detecting GFPs. The authors analyze various aspects of the behavior of fission products in a liquid-metal-cooled reactor, such as the movement of GFPs in dissolved and bubble form along the circuit, the sorption of volatile FPs in the lead coolant (LC) and on the surfaces of structural elements, degassing of the GFPs dissolved in the LC, and filtration of cover gas from aerosol particles of different nature. In addition, a general description is given of the conditions for the transfer of GFPs in a LC environment of the reactor being developed. Finally, a mathematical model is presented that makes it possible to determine the calculated activity of reference radionuclides in each reactor unit at any time after the fuel element tightness failure. Based on this model, methods for monitoring the fuel cladding tightness by the gas activity in the gas volumes of the reactor plant will be proposed.