  The influence of a massive Majorana tau-neutrino on primordial
nucleosynthesis is rigorously calculated. The system of three
integro-differential kinetic equations is solved numerically for the
tau-neutrino mass in the interval from 0 to 20 MeV. It is found that the usual
assumption of kinetic equilibrium is strongly violated and non-equilibrium
corrections considerably amplify the effect. Even a very weak restriction from
nucleosynthesis, allowing for one extra massless neutrino species, permits to
conclude that m_\nu_\tau < 1 MeV. For a stricter bound, e.g. for dN < 0.3, the
limit is m_\nu_\tau < 0.35 MeV.
