  The structure of the deflagration burning front in type Ia supernovae is
considered. The parameters of the flame are obtained: its normal velocity and
thickness. The results are in good agreement with the previous works of
different authors. The problem of pulsation instability of the flame, subject
to plane perturbations, is studied. First, with the artificial system with
switched-off hydrodynamics the possibility of secondary reactions to stabilize
the front is shown. Second, with account of hydrodynamics, realistic EOS and
thermal conduction we can obtain pulsations when Zeldovich number was
artificially increased. The critical Zeldovich numbers are presented. These
results show the stability of the flame in type Ia supernovae against
pulsations because its effective Zeldovich number is small.
