This paper addresses the behavior of a candle flame in a long-duration, quiescent microgravity environment both on the space Shuttle and the Mir Orbiting Station. On the Shuttle, the flames became dim blue after an initial transient where there was significant yellow (presumably soot) in the flame. The flame lifetimes were typically less than 60 seconds. The safety-mandated candlebox that contained the candle flame inhibited oxygen transport to the flame and thus limited the flame lifetime. The flames on the Mir were similar, except that the yellow luminosity persisted longer into the flame lifetime because of a higher initial oxygen concentration;The Mir flames burned for as long as 45 minutes. The difference in the flame lifetime between the Shuttle and Mir flames was primarily the redesigned candlebox that did not inhibit oxygen transport to the flame. In both environments, the flame intensity and the height-to-width ratio gradually decreased as the ambient oxygen content in the sealed chamber slowly decreased. Both sets of experiments showed spontaneous, axisymmetric flame oscillations just prior to extinction. The paper also presents a numerical model of a candle flame. The formulation is two-dimensional and time-dependent in the gas phase with constant specific heats, thermal conductivity and Lewis number (although different species can have different Lewis numbers), one-step finite-rate kinetics, and gas-phase radiative losses from CO2 and H2O. The treatment of the liquid/wick phase assumes that the fuel evaporates from a constant diameter sphere connected to an inert cone. The model predicts a steady flame with a shape and size quantitatively similar to the Shuttle and Mir flames. The computation predicts that the flame size will increase slightly with increasing ambient oxygen mole fraction. The model also predicts pre-extinction flame oscillations if the rate of decrease in ambient oxygen is small enough, such as that which would occur for a flame burning in a sealed ambient.