With the compelling evidence for massive neutrinos from recent neutrino oscillation experiments, one of the most fundamental tasks of particle physics over the next years will be the determination of the absolute mass scale of neutrinos, which has crucial implications for cosmology, astrophysics and particle physics. Neutrino oscillation experiments can measure squared mass differences but not masses. The latter have to be determined in a different way. The direct mass experiments investigate -- besides time-of-flight measurements -- the kinematics of weak decays obtaining information on the neutrino mass without further requirements. Here the tritium beta decay experiments give the most stringent results. The current tritium beta decay experiments at Mainz and Troitsk are reaching their sensitivity limit. The different options for a next generation direct neutrino mass experiment with sub-eV sensitivity are discussed. The KATRIN experiment, which will investigate the tritium beta spectrum with a MAC-E-Filter of 1 eV resolution, is being prepared to reach a sub-eV sensitivity.
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