In this master thesis the emphasis was set on the detection of trace amounts of 93-Zr as a representative of long-lived fission products (T1/2 = 1.64·10^6 a). Because of its trace concentration in many samples, its measurement is a matter of difficulty for most of the detection methods. Only accelerator mass spectrometry can measure ultra low concentrations. The isotopic separation of 93-Zr from its stable neighboring isotopes and the isobaric separation from 93Nb have been investigated and optimized. The measurements were carried out with the Accelerator Mass Spectrometry (AMS) set-up at the Maier-Leinbnitz Laboratorium in Garching, Germany. The main experiment was conducted with the Time-of-Flight beam line, using passive absorbers of different thicknesses in form of a stack of silicon nitride foils. Ion beams with high energies, between 80 and 170 MeV were utilized for the measurements. In order to theoretically determine the optimal foil thickness, the simulation program SRIM and numerical calculations with stopping power tables were used. Due to the discrepancies in the results an experimental determination has been performed. This led to optimization of the set-up. The achieved detection limit for 93-Zr was 93-Zr/Zr = 1.7·10^(-10), presently the lowest value for the detection of 93Zr. The stopping power of the stable 92-Zr and 94-Zr was also investigated and verified. 93-Zr is one example of long-lived fission product, additional measurements with 99-Tc were performed. They showed promising results for the implementation of the passive absorber method as a detection technique for ultra trace amounts of a long-lived radioisotope in the mass range around 100 amu. Additionally, an experimental determination of the separation of 93Nb versus 93-Zr by means of a gas filled magnet was made. In order to reduce the isotopic and isobaric background, tests were carried out with different pressure combinations in the magnet chamber and in the detector. Optimizing the conditions led to a detection limit of 93-Zr/Zr = 4.7·10^(-10), comparable to the results with the Timeof-Flight beam line. The results represent the lowest detection limit achieved for 93-Zr, without prior chemical processing of the used samples.