  We study the nonresonant oscillations between left-handed electron neutrinos
nu_e and nonthermalized sterile neutrinos nu_s in the early Universe plasma.
The case when nu_s do not thermalize till 2 MeV and the oscillations become
effective after nu_e decoupling is discussed. The evolution of neutrino
ensembles was described numerically by integrating the kinetic equations for
the neutrino density matrix in momentum space. We have provided a detail
numerical study of the influence of the nonequilibrium nu_e - nu_s oscillations
on the primordial production of He-4. The exact kinetic approach enabled us to
calculate the effects of neutrino population depletion, the distortion of the
neutrino energy spectrum and the generation of neutrino-antineutrino asymmetry
on the kinetics of neutron-to-proton transitions during the primordial
nucleosynthesis epoch and correspondingly on the cosmological He-4 production.
  It was shown that the neutrino population depletion and spectrum distortion
play an important role. The asymmetry effect, in case the lepton asymmetry is
accepted initially equal to the baryon one, is proved to be negligible for the
discussed range of delta m^2. Constant helium contours in delta m^2 - theta
plain were obtained for small mass differences delta m^2 < 10^{-7} eV^2. More
precise cosmological constraints on mixing parameters were obtained.
