The search for the neutrino mass by direct method in the tritium beta-decay and perspectives of study it in the project KATRIN

The updated results of the search for neutrino mass in the tritium beta-decay on the Troitsk nu-mass and Neutrino Mainz set-ups are presented. Both groups give an upper limit for the neutrino mass at 95% m(v) < 2.05 eV/c(2) in Troitsk and m(v) < 2.2 eV/c(2) in Mainz. Further improvement is limited both by statistic and systematic errors. In order to enter in the cosmologically important sub-electronvolt area the collaboration of groups from Karlsruhe Forschungszentrum, Mainz, Troitsk et al. proposed a new advanced project KATRIN. The status of the project is presented.