Instability of the detonation wave in the degenerate core of a star is
studied. It appears, that nearly the whole core is burned up in an un
stable detonation regime. The kinetics of thermonuclear burning in the
se conditions probably leads to a chemical composition of the supernov
a remnant, differing from that obtained for the case of stationary pro
pagation of the wave. It is necessary, therefore, to develop mathemati
cal supernova models with the burning front defined according to the m
odel by Zeldovich-von Neuman-Dering. Furthermore, the existence of an
unstable detonation regime suggests that the detonation may come to a
half.