The television program Firefly is set 500 years in the future when only America and China survive and form one super- power called the alliance. The alliance fight the 'brown coats', those fighting for independence. They win and everything becomes regulated by this global super-power. As a result of this everyone can speak Chinese and English but these languages have merged. In Firefly characters fluently chop and change between the two languages.
Although the show does not explain why the alliance is based on American and Chinese power it is an American show and showing America as in decline or defeated by the Chinese super power would probably harm ratings. However I think the concept of America and China forming one super power is interesting and definitely couldn't be ruled out in the next 500 years.