The controllable active thermo-atmosphere combustor(CATAC) has become a utilizable and effective facility because it benefits the optical diagnostics and modeling. This paper presents the modeling research of the auto-ignition and flames of the H2/N2(H2/CH4/N2,or H2/H2O2/N2) mixture on a CATAC,and shows curves varying with temperatures of auto-ignition delay,the height of the site of auto-ignition of lifted flames,and flame lift-off height. The results of auto-ignition delay and the lift-off height are compared the experimental results to validate the model. A turning point can be seen on each curve,identified with criterion temperature. It can be concluded that when the co-flow temperature is higher than the criterion temperature,the auto-ignition and lifted flame of the mixture are not stable. Conversely,below the criterion temperature,the mixture will auto-ignite in a stable fashion. Stabilization mechanisms of auto-ignition and lifted flames are analyzed in terms of the criterion temperature. The controllable active thermo-atmosphere combustor (CATAC) has become a utilizable and effective facility because it benefits the optical diagnostics and modeling. This paper presents the modeling research of the auto-ignition and flames of the H2 / N2 (H2 / CH4 / N2 , or H2 / H2O2 / N2) mixture on a CATAC, and shows curves varying with temperatures of auto-ignition delay, the height of the site of auto-ignition of lifted flames, and flame lift-off height. The results of auto- ignition delay and the lift-off height are compared the experimental results to validate the model. A turning point can be seen on each curve, identified with criterion temperature. It can be concluded that when the co-flow temperature is higher than the criterion temperature , the auto-ignition and lifted flame of the mixture are not stable. Conversely, below the criterion temperature, the mixture will auto-ignite in a stable fashion. Stabilization mechanisms of auto-ignition and lifted flames are analyzed in terms of the criterion t emperature.