The extension of the quasi-steady radially symmetric theory of liquid-droplet vaporization and homogeneous combustion to solid fuels and additives requires several basic modifications. One relatively simple extension, undertaken here, permits the gasification process al the two-phase interface to be modelled not by adiabatic sublimation, but by finite-rate heterogeneous chemical reaction. Such an extension by itself allows the burning of solid spheres of carbon to be adequately described. In particular, for carbon spheres, surface reactions involving production of carbon monoxide (by consumption of oxygen or by reduction of carbon dioxide) and of carbon dioxide (by consumption of oxygen) may be coupled with a bipropellant homogeneous reaction between carbon monoxide and oxygen. More general results for the net mass transfer rate (the Sherwood number) with nonequilibrium reversible heterogeneous reactions than previously obtained are presented. Further, closed-form results are derived for special cases of simultaneous gas-phase and surface reactions. Invariance of the Sherwood number to details of the chemistry in several circumstances indicates that gross agreement between theory and experiment is possible even with incorrect models of the kinetics. Finally, reasons for the success of “additive times” in predicting lifetimes of particles gasified under rate processes are presented.