  We present results of a linear stability analysis of relativistic detonation
fronts, which have been considered as representing phase interfaces in
cosmological first order phase transitions. After discussing general stability
conditions for detonation fronts, we concentrate on the properties of the
fronts with respect to corrugation instabilities and discuss separately the
cases of Chapman-Jouguet and strong detonation waves. Contrarily to what
recently claimed, we find that strong detonations are both evolutionary and
stable with respect to corrugations of the front. Moreover, Chapman-Jouguet
detonations appear to be unconditionally linearly stable. The implications of
the stability results for first order cosmological phase transitions are
presented and a discussion of the causal structure of reaction fronts is also
given.
