  We show that, if they exist, lepton number asymmetries ($L_\alpha$) of
neutrino flavors should be distinguished from the ones ($L_i$) of mass
eigenstates, since Big Bang Nucleosynthesis (BBN) bounds on the flavor
eigenstates cannot be directly applied to the mass eigenstates. Similarly,
Cosmic Microwave Background (CMB) constraints on mass eigenstates do not
directly constrain flavor asymmetries. Due to the difference of mass and flavor
eigenstates, the cosmological constraint on the asymmetries of neutrino flavors
can be much stronger than conventional expectation, but not uniquely determined
unless at least the asymmetry of the heaviest neutrino is well constrained.
Cosmological constraint on $L_i$ for a specific case is presented as an
illustration.
