The cosmic energy density in the form of radiation before and during Big Bang Nucleosynthesis (BBN) is typically parameterized in terms of the effective number of neutrinos Neff. This quantity, in case of no extra degrees of freedom, depends upon the chemical potential and the temperature characterizing the three active neutrino distributions, as well as by their possible non-thermal features. In the present analysis we determine the upper bounds that BBN places on Neff from primordial neutrino-antineutrino asymmetries, with a careful treatment of the dynamics of neutrino oscillations. We consider quite a wide range for the total lepton number in the neutrino sector, ην = ηνe+ηνμ+ηντ and the initial electron neutrino asymmetry ηνein, solving the corresponding kinetic equations which rule the dynamics of neutrino (antineutrino) distributions in phase space due to collisions, pair processes and flavor oscillations. New bounds on both the total lepton number in the neutrino sector and the νe−bar nueasymmetry at the onset of BBN are obtained fully exploiting the time evolution of neutrino distributions, as well as the most recent determinations of primordial 2H/H density ratio and 4He mass fraction. Note that taking the baryon fraction as measured by WMAP, the 2H/H abundance plays a relevant role in constraining the allowed regions in the ην−ηνein plane. These bounds fix the maximum contribution of neutrinos with primordial asymmetries to Neff as a function of the mixing parameter θ13, and point out the upper bound Neff≲3.4. Comparing these results with the forthcoming measurement of Neff by the Planck satellite will likely provide insight on the nature of the radiation content of the universe.