  We re-examine neutrino oscillations in the early universe. Contrary to
previous studies, we show that large neutrino asymmetries can arise due to
oscillations between ordinary neutrinos and sterile neutrinos. This means that
the Big Bang Nucleosynthesis (BBN) bounds on the mass and mixing of ordinary
neutrinos with sterile neutrinos can be evaded. Also, it is possible that the
neutrino asymmetries can be large (i.e. $\stackrel{>}{\sim} 10\%$), and hence
have a significant effect on BBN through nuclear reaction rates.
