Extinction and cellular instabilities are investigated in premixed tubular flames. A tubular burner has recently been designed and constructed to be capable of operating under a wide range of conditions that allow more accurate and detailed study of tubular premixed and non-premixed flames. Extinction measurements of tubular flames can be carried out through the entire equivalence ratio spectrum for various types of fuels without introducing serious turbulent effects. In this study, the extinction conditions of premixed tubular flames generated by H2/O2 or CH4/O2 mixed with various inert diluents (Ar, CO2, N2) and enriched oxygen are measured. In addition, the onset conditions for flame instability at different cell numbers are reported. Petal shaped cellular flames with symmetric regions of local extinction are observed for lean H2 tubular flames with low Lewis numbers. Wrinkled flames with no local extinction are observed for nearly equidiffusive lean CH4 tubular flames. The combined effects of curvature, diffusive-thermal instability and hydrodynamics are thought to be responsible for the cellular structure. The lack of extinction in the nearly equidiffusive lean CH4 tubular flames indicate that strong diffusive-thermal effects due to non-unity Lewis number are required to produce local extinction in the cellular structure of tubular flames.