China's Nationality Law states that China does not recognize dual nationality. A Chinese citizen who voluntarily acquires foreign nationality automatically loses Chinese nationality. So holding "two passports at once" is not recognized in China.
For travel: after naturalization, your first trip back to China requires a China visa in your foreign passport. If you exit on a Chinese passport, you may be stopped on return, which can even affect future applications.
If you do not want to give up your Chinese status, consult Chinese law before naturalizing; some people choose a green card instead of citizenship. Policies differ by country — seek professional legal advice.
