The flame speed in vortex rings of methane/air and propane/air mixtures has been measured bya high speed video camera and the maximum tangential velocity in the vortex ring has been estimated from the hot-wire measurements on the cold-air vortex rings. Results show that in accordance with the back-pressure drive flame propagation mechanism the flame speeds increase almost linearly with the maximum tangential velocity and their slopes are around unity for all the lean, stoichiometric and rich mixtures investigated. However, it is found that the flame speed is lowered down when the flame diameter becomes small, and the flame can never propagate in lean mixtures if the flame diameter becomes less than the order of the laminar flame thickness. Also, it is found that in the near rich-limit methane/air mixture the flame speed becomes almost constant independently of the maximum tangential velocity. It would appear that the flame should propagate in the mixing zone with the ambient air.