Carbon-oxygen thermonuclear detonations in supernovae are unstable at
densities above congruent-to 2 x 10(7) g cm-3 with respect to longitud
inal perturbations. The instability is caused by the positive feedback
between hydrodynamical fluctuations and the energy release in the C-1
2 + C-12 reaction. The question remains open whether the detonations a
re stable or not at densities below 2 x 10(7) g cm-3. The implications
of the instability to the initiation of detonations in supernovae and
supernovae nucleosynthesis are discussed.