The possibilities of identifying the fuel elements and fuel assemblies from the cores of first-generation research reactors in the USSR (F1, TVR, RFT, IGR, and IVG.1) and USA BGRR, EBR I, MTR, ARE, and TREAT) are examined. The fuel elements and assemblies are described and the cross section and characteristic dimensions are presented. It is shown that the fuel elements and fuel assemblies are different and that in order to identify them in most cases only the geometric dimensions need by examined and measured. However, if a reactor fuel element or assembly is completely destroyed, then the uranium enrichment and isotopic composition as well as the impurity composition must be measured.In recent years, there have been cases of trafficking in nuclear materials [1]. In 2005, there were 101 cases of unauthorized activity involving nuclear and radioactive materials -18 cases involved nuclear, 76 radioactive, and 7 radioactively contaminated materials [2]. From the standpoint of the threat from terrorism, the rare cases involving radioactive materials are not of great concern but the actions taken against trafficking should not depend on the number of events that have occurred, since the consequences of even a single unlawful use such material can be serious.Since 1942, approximately 660 research reactors have been built, including about 250 in the US, and more than 100 research reactors and critical assemblies were operated in the USSR. Their fuel can attract wrongdoers because it is often fabricated from high-enrichment uranium. When nuclear material of unknown origin is detained, it must be identified in order to determine the sites of production, operation, misappropriation and suppression of subsequent illegal acts. Countermeasures against trafficking of nuclear materials, and in particular identification, are topical matters, in connection with which the term