This paper presents the results of theoretical calculations fur radiation-induced extinction of one-dimensional unsteady diffusion flames in a quiescent microgravity environment. The model formulation includes both gas and soot radiation. Soot volume fraction is not a priori assumed, instead it is produced and oxidized according to the temperature- and species-dependent formation and oxidation rates. Thus, soot volume fraction and the resulting: flame radiation varies with space and time. Three cases are considered: (i) a nonradiating Flame, (ii) a barely sooty Hams, and (iii) a very sooty flame. For the nonradiating flame, the maximum flame temperature remains constant and it does not extinguish. However. the burning rate decreases with time (t) as t(1/2) making the flame "weaker." For radiating flames, the flame temperature decreases due to radiative heat loss fur both barely sooting and heavily sooting flames. resulting in extinction. The decrease in the burning rate for radiating flames is also much faster than t(1/2). Surprisingly, gas radiation has a larger effect on the flame temperature than soot radiation in this Flame configuration. This is because the gaseous combustion products (primarily CO2 and H2O) accumulate in the high-temperature reaction zone, while the soot exists in the low-temperature region on the fuel side. Also, the soot region is comparatively narrower and the soot volume fraction decreases with time due to oxidation by CO2 and H2O. At early times, before a significant increase in the concentrations of CO2 and H2O. large amounts of soot are formed and the radiation from soot is also very large. However, this radiative heat loss clues not cause a perceptible local depression in the temperature profile because it is offset primarily by thermal diffusion and to a lesser degree by heat release due to soot radiation. Later, both soot and soot radiation decrease with time. These results are consistent with the experimental observations made in microgravity spherical diffusion flames and provide considerable insight into radiative cooling of sooty flames. This work, while nut experimental, does shows that radiative extinction of diffusion flames in a quiescent microgravity environment is possible.