We examine the dynamic characteristics of the diffusion flame surround
ing a droplet of liquid fuel in a reduced oxidant environment. The stu
dy is motivated by the experimental observations of candle flames in m
icrogravity, which bear some similarity to the spherical diffusion fla
me that surrounds a burning liquid fuel droplet. The microgravity expe
riments reveal that, when the oxidant concentration in the chamber is
sufficiently low, oscillations develop before extinction, A similar ph
enomenon is predicted here. An oscillatory state results for a suffici
ently low oxidant concentration when radiative losses from the name ar
e appreciable. The frequencies of oscillations we predict are in good
agreement with the experimental observations.