The review summarizes the long-term experience in theoretical research of combustion of gasifying condensed systems with periodically varied pressure. Most results are obtained within the framework of the Zel'dovich-Novozhilov theory. The main properties of the linear function of the burning rate response to harmonically varied pressure are discussed. The concept of nonlinear response functions is introduced, which is illustrated by the explicit form of a number of second-order response functions. A new phenomenon is described: bifurcations of response functions with a varied amplitude or frequency of pressure oscillations. For the simplest gunpowder model containing three parameters only, the sequence of bifurcations of doubling of the burning rate oscillation period is studied, which finally leads to a random combustion regime. An analytical relation between the linear response functions to harmonically varied pressure and to an oscillating radiant heat flux is noted. An example of calculating the response function with allowance for thermal inertia of the gas phase is presented.

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-Besides being of technological importance, the SHS processes are also very interesting from the scientific standpoint. For gasless and filtration combustion i t was shown in the linear approximation that instability of steady-state regimes with multidimensional perturbations arises more readily than in the one-dimensional case. A s a result beyond the scope of the linear approximation the theory predicts a wide spectrum of very peculiar nonsteady burning regimes such as oscillatory combustion or spin waves. In the last twenty years many problems involving in steady-state and nonstationary SHS flame propagation have been investigated both theoretically and experimentally. The main objective of this presentation is t o provide a review of recent developments in nonsteady non-linear SHS phenomena. The following topics a r e considered: experimental investigation of the non-steady regimes, stability of steady-state regimes, nonsteady autowave phenomena and their classification, and the possibility of chaotic behavior.Analytical and numerical results pertaining t o these problems a r e discussed in brief. Experimental results available in the literature are compared with those inferred from analytical and/or numerical studies. I t is concluded that the theoretical results cannot be regarded as quite satisfactory f o r the explanation of information obtained from experimental studies. Areas of future studies are also discussed.