We discuss the stability of a deflagration front in white dwarfs in th
e context of burning mechanisms for Type Ia Supernovae. It is shown th
at the basic characteristics of the instability of the deflagration fr
ont are different from those of Rayleigh-Taylor instability, on which
the deflagration models rely. In view of this, together with results f
rom two-dimensional simulations, we argue that the deflagration model
needs reconsideration, as Rayleigh-Taylor instability cannot explain t
he required high flame speed required for producing an explosion simil
ar to Type Ia Supernovae. On the other hand, the same arguments imply
that delayed detonation is acceptable and that the transition to deton
ation must occur in the very low density regime, where good agreement
between observations and numerical results is obtained.