This article analyzes some prospects for the economic and political development of the United States and China. The first part of the article is devoted to the consideration of strengths and weaknesses of the U.S. model and of the Chinese one. The second part of the article considers the most probable scenarios of the future struggle for world leadership. The first scenario suggests that China will continue developing at a faster rate in the several coming decades and will be gradually catching up with the United States in terms of Gross Domestic Product (GDP) production. However, after several crises in 2008–2020 the United States will likely regain a number of advantages over China as a result of assimilation of the newest technologies. The second scenario suggests that the United States will come across a whole range of internal social and political problems related to internal political splits. In this case, the United States will have to share its global leadership with China. The article attempts to answer the following questions: What scenario is more probable? Will the old world order change? What are the main conclusions for the European Union and for Russia?