The Mainz neutrino-mass experiment investigates the endpoint region of the
tritium beta-decay spectrum with a MAC-E spectrometer to determine the mass
of the electron antineutrino. By the recent upgrade, the former problem of
dewetting T-2 films has been solved, and the signal-to-background ratio wa
s improved by a factor of 10. The latest measurement leads to m(nu)(2) = -3
.7 +/- 5.3(stat.) +/- 2.1(syst.) eV(2)/c(4), from which an upper limit of m
(nu) < 2.8 eV/c(2) (95% C.L.) is derived. Some indication for the anomaly,
reported by the Troitsk group, was found, but its postulated half-year peri
od is contradicted by our data. To push the sensitivity on the neutrino mas
s below 1 eV/c(2), a new larger MAC-E spectrometer is proposed. Besides its
integrating mode, it could run in a new nonintegration operation MAC-E-TOF
mode. (C) 2000 MAIK "Nauka/Interperiodica".