The quasi-steady adiabatic vaporization and subsequent exothermic decomposition of a pure monopropellant spherical droplet is examined in the absence of free and forced convection. The Lewis number is fixed at unity and linear variation of the universal diffusion coefficient with temperature is adopted. A direct one-step first-order decompositional burning is postulated. By means of inner-and-outer (matched asymptotic) expansions the vaporization rate is analytically determined for cases in which the ambient atmosphere is inert with respect to the product of decomposition. Both the case of very large and very small first Damkohler number is considered (where the first Damkohler number is the ratio of the rate of reaction to the rate of mass diffusion). Then a two-step irreversible reaction model is examined for the case in which the ambient atmosphere is reactive, in bipropellant fashion, with the product of decomposition. Conditions for sequential concentric flames are described.