Solid-solid combustion becomes self-sustaining when the preheating of the fresh mixture is high enough to support a spontaneous chemical reaction. These reactions have high activation energies, requiring significant preheating. Traditionally, conduction has been considered as the main form of preheating, and propagation velocities in the order of a few mm to a few cm per second were found. When acoustic equations are included in the analysis, no significant changes occur for traditional SHS reactions. However, the analysis of a 1-D model propagating at a constant velocity reveals the existence of two other solutions with propagation velocities which are much faster. An SHS deflagration wave is found with combustion temperature lower than the adiabatic value. The propagation velocity is less than the longitudinal sound speed of the medium, but typical Mach numbers vary between 0.6 and 0.95. The third solution is an SHS detonation with temperature above the adiabatic value and supersonic propagation velocity. Since the heat fluxes are extremely high, the hyperbolic conduction model is used.