  We study the distortion of electron neutrino energy spectrum due to
oscillations with the sterile neutrino nu_e <-> nu_s, for different initial
populations of the sterile state delta N_s at the onset of oscillations. The
influence of this spectrum distortion on Big Bang Nucleosynthesis is analyzed.
Only the case of an initially empty sterile state was studied in previous
publications.
  The primordial abundance of He-4 is calculated for all possible delta N_s:
0<= delta N_s<= 1 in the model of oscillations, effective after electron
neutrino decoupling, for which the spectrum distortion effects on the
neutron--proton transitions are the strongest.
  It is found that the spectrum distortion effect may be the dominant one not
only in the case of small delta N_s, but also in the case of big initial
population of nu_s. For example, in the resonant case it may play a
considerable role even for very big delta N_s ~ 0.8.
