The combined effects of flame curvature, radiation, and stretch on the extinction of premixed tubular flames are investigated by using the large-activation-energy asymptotic method with a non-linear radiation model. A general expression for flame speed, flame temperature and extinction limits is obtained and it is used to study the radiation and flame curvature coupling at different Lewis numbers. The results show that the coupling between radiation and flame curvature leads to multiple flame bifurcations and extinction limits. Furthermore, both the stretch and radiation extinction limits are found to be greatly affected by flame curvature. (C) 2008 Elsevier Ltd. All rights reserved.