The flame stability limits of confined jet diffusion flames (JDFs) flowing into a co-axial oxidizing stream was studied both experimentally and analytically. Methane and hydrogen and their mixtures were used as the fuel. The experiments were conducted with two different jet diameters and within a wide range of co-flowing stream velocities and hydrogen concentrations in methane or air stream. The hydrogen diffusion flame was found to have a much larger region of stable operation than the methane JDF. Higher stability of the methane JDFs was achieved by the addition of hydrogen to either the jet fuel or the surrounding air stream. A hysteresis phenomena were observed in the reattachment process of lifted flames. It was found that the conditions-prior to ignition of the flame, such as the value of co-flowing stream and jet velocities and position of the ignitor, have significant effect on the type of flame stabilization mechanism and flame blowout limits. The optimum ignition conditions for achieving higher blowout limits were investigated. The blowout limits of lifted JDFs were significantly affected by the velocity of co-flowing stream. The present study also reports the results of the calculation of the blowout limits of lifted JDFs using as a criterion the ratio of mixing time scale to characteristic combustion time scale. The agreement of the experimental and calculated data was satisfactory.