Reaction propagation of ethylene/oxygen and methane/oxygen mixtures in capillary tubes of 1 and 2 mm in diameters with initial pressure and temperature at ambient condition were experimentally visualized and analysed using high speed cinematography. Deflagrative flame was initiated in middle of the smooth tube, and the reaction fronts accelerated as they propagated towards the exits in the opposite directions. Lengths of the tubes investigated ranged from 0.4 to 1 m (one side), and deflagration-to-detonation transitions were observed for equivalence ratios between 0.5 and 3. The visible reaction front propagates at speeds approach Chapman-Jouguet speed for ethylene/oxygen mixture in the 1 mm and 2 mm tubes. An overshoot in propagation velocity was found during transition process. For leaner and richer mixtures beyond the detonation limits, steady deflagration wave propagation was observed. Reaction propagation in methane/oxygen mixture was also investigated. Several near-limit propagation modes were found.