  We present a linear analysis of acoustic and thermo-reactive instabilities in
a diffuse gas, photoionized and heated by a radiation field, cooled by
collisional excitation of hydrogen and metal lines. The hydrogen recombination
reaction has a stabilizing effect on the thermal mode found by Field (1965)
since the condensation instability occurs in a narrower region of the parameter
space and grows on longer time scales due to its oscillatory character. This
effect is stronger when the mean photon energy is not much larger than the
hydrogen ionization energy. Moreover, for fixed values of thermal pressure and
photoionization rate, there are thermo- reactive unstable equilibria for which
no transition to a stable phase is possible. By extending our analysis of the
thermo-reactive modes to the nonlinear regime we show that when no phase
transition is possible the medium evolves through a series of nonequilibrium
states characterized by large amplitude, nonlinear periodic oscillations of
temperature, density and hydrogen ionization fraction. We find also unstable
acoustic waves which, for solar metal abundances, are the fastest growing modes
in two temperature intervals: around $T\sim 100$~K and $T\sim 8000$~K (i.e.
cold and warm phase, respectively), independent of the mean photon energy.
Possible implications for the interstellar medium and intergalactic medium are
briefly outlined.
