Theoretical analyses are developed for the multiphase deflagration of porous energetic solids, such as degraded nitramine propellants, that experience significant gas how in the solid preheat region and are characterized by the presence of exothermic reactions in a babbling melt layer at their surfaces. Relative motion between the gas and condensed phases is taken into account in both regions, and expressions fur the mass burning rate and other quantities of interest, such as temperature and volume-fraction profiles, are derived by activation-energy asymptotics. The model extends recent work by allowing for gas flow in the unburned solid, and by incorporating pressure effects through the gas-phase equation of state. As a consequence, it is demonstrated how most aspects of the deflagration wave, including its structure, propagation speed, and final temperature, depend on the local pressure in the two-phase regions.