Is China politically stable?

Yes. People's Republic of China is ruling by Communist Party of China. With the theory of democratic centralism, China adopted one-party-ruling political system without presidential-elections as western countries. President of China is elected in People's Congress. Most Chinese are comparatively satisfied with this system. So China is politically stable in recent years. I would happen to disagree;

China is in - but maybe not stable On a daily basis, China attracts attention worldwide. Our businesses outsource manufacturing, services and innovation to China and ministers queue up to visit and show their respect to the Middle Kingdom. China's President, Communist Party General Secretary and Military Leader, Hu Jintao, and other forth generation communist leaders manifest their power while struggling to keep everything together. Most recently, one of their colleagues was removed from the post as Communist Party Secretary in Shanghai, one of China's top posts, accused of corruption and mishandling of power. In fact, challenges are piling up as tall as Shanghai's skyscrapers: increasing income differentials due to China's 'wild west capitalism', social and political unrest across the country, pollution, shortage of energy, horrendous lack of social welfare etc.

So if you think about it, it isn't really stable.