Common tunable CW 002 lasers only have limited output power with unstable branch and intensity due to the environment variations which will cause the branch jumping and the intensity fluctuation predominantly. But the branch and intensity stabilities are rather important for many applications as same as high power output. In a previous paper1113, we have reported that the output more than SOW with a folded compound cavity was obtained. In the present paper, we report the influences of the folded compound cavity on both the branch and intensity stabilities. With this cavity, the folded compound cavity configuration will show some frequency characteristics and compensation effect for the variation of the environmental condition, and hence long-term stability of the branch and the intensity output are obtained. We have observed that the output power fluctuation was less than 5% with branch stabilized for a relaxed environment conditions as the fluctuations of discharge current in the plasma tube within 2mA, the temperature of cooling water within 1.5 ℃ and the room temperature within 3 ℃. We find that there will be an inherent automatism effect for stability controlling of the branch by suitable initial setting of the cavity, and this novel phenomenon is discussed and explained also.