We compute the nucleosynthesis bounds on the masses of stable Dirac and Majorana neutrinos by solving an evolution equation network comprising of all neutrino species which in the Dirac case includes different helicity states as separate species. We will not commit ourselves to any particular value of the nucleosynthesis bound on the effective number of light neutrino degrees of freedom Nv, but present all our mass bounds as functions of ΔNv. For example, we find that the excluded region in the mass of a Majorana μ- or τ-neutrino, 0.29 MeV < mMv < 53 MeV corresponding to a bound ΔNv < 0.3 gets relaxed to 0.95 MeV < mMv < 32 MeV if ΔNv < 1.0 is used instead. For the Dirac neutrinos ΔNv < 1.0 gives the upper limits (for TQCD = 100 MeV) mDvμ < 0.31 MeV and mDv- < 0.37 MeV and the lower limit mDv > 25 MeV. Together with the present experimental limit nucleosynthesis excludes mMvτ > 0.95 MeV and mDvτ > 0.37 MeV at 95% CL.