Neutron activation analysis methods for the determination of impurities in zirconium cladding material and uranium oxide are described. Detection limits for the elements Al, Cd, Cr, Co, Cu, Hf, Fe, Mn, Ni, W and U in zirconium are below that required by the ASTM B 352-79 standard. The method has been tested on the NIST SRM 360a Zircaloy-2 from which the elements Na, Mg, Al, Ca, V, Cr, Fe, Co, Ni, Cu, Eu and U have been detected. The values for Cr, Fe, Ni and Cu are compared with the certified values. A method for the pre-irradiation separation of the elements Mg, Na, Al, K, Sc, Ca, V, Mn, Cr, Fe, Co, Cu, Zn, Rb, Zr, Cd, Cs, REE and Hf from uranium has been developed. A neutron activation analysis method for the determination of those elements in uranium is described. The method is tested by the analysis of the IAEA reference sample SR-54/64. The elements Al, Mn, V, Cu, Cr, Co, Ni and Fe have been detected and the results compared with the certified values.