The flame stability limits essentially define the fundamental operation of the combustion system. The critical conditions at the stability limits are highly dependent on flow configurations and some species of fuels. For various species of fuels (Methane, Propane and Hydrogen), the flame-base stability mechanism for flame holding has been studied. In this study, the transition behavior from the stable flame to lifting and blow-off is observed experimentally with the co-flowing air at each oxygen concentration. The lifting and blow-off criteria are proposed for the spout diffusion flame with co-flowing air. The results obtained are as follows. The color of a flame become dimmer and lifting velocity is lower, when oxygen concentration of co-flowing air become lower.