Using a laser Doppler velocimetry, relationships between the flame speed, V f , and the maximum tangential velocity, V hmax , in vortex ring combustion of hydrogen/air mixtures have been rigorously obtained. Results in the air atmosphere show that the slopes in the V f β«Χβ¬ V hmax plane are almost unity for lean mixtures, whereas the slope increases, contrary to the vortex bursting theory, with an increase in the equivalence ratio for rich mixtures. The flame speeds for lean mixtures are in good agreement with the back-pressure drive flame propagation theory, whereas the flame speeds for rich mixtures become much higher than the values given by the back-pressure drive flame propagation theory and approach the predictions of the vortex bursting theory. To clarify the basic cause of the enhancement of flame speed, further measurements have been made in a nitrogen atmosphere. Results show that the flame speeds for rich mixtures are lowered and they are in good agreement with the back-pressure drive flame propagation theory. Thus, it is confirmed that the enhancement of flame speed in air is attributed to the combustion of excess hydrogen with the ambient air. The mechanism for the enhancement of flame speed has been discussed on the basis of a steady-state flame propagation model for vortex ring combustion. It is shown that if we assume that the excess hydrogen is burned with a turbulent burning velocity, which is proportional to the maximum tangential velocity, and that the pressure behind the flame is additionally raised, then the increase in slope in the V f β«Χβ¬ V hmax plane can be well described.