  The effect of particles that undergo strong diffusive-shock-acceleration on
the stability of the accelerating shock is investigated. A two-fluid model is
employed in which the accelerated particles are treated as a fluid whose effect
is incorporated as an additional pressure in the momentum equation. The Dyakov
and Kontorovich stability criteria are used in order to study the stability of
those steady-state shocks that contain a gas sub-shock. The downstream
conditions of the latter are parametrized by the ratio of the upstream
acclerated-particles pressure to the total pressure. For some range of values
of that parameter, three possible downstream states are possible for each
upstream state. It is shown that in that range of parameters the shocks are
either corrugationally unstable or lose their energy by spontaneous emission of
acoustic as well as entropy-vortex waves.
