With United States President Barack Obama and Secretary of State Hillary Clinton back in Washington after their swings through the Pacific and Asia, the giant amphibious assault ship, USS Essex, slipped into Hong Kong this week.
This is taking care of business: China suspended military ties with the US in February over arms sales to Taiwan and had been none too pleased by Washington's intervention in its territorial disputes in the South China Sea and elsewhere - not to mention the tensions over trade and currency demands.
But the two Asia-Pacific giants accept that they need to get on even as they compete to build their own influence across the region.
"It is not in anyone's interests for the US and China to see each other as adversaries," Clinton said during her Australian visit.
"We do look forward to working closely with China, bilaterally and through key institutions, as it takes on a greater role and, at the same time, takes on more responsibility in regional and global affairs."
For countries much closer to Beijing, China's shadow is more threatening.
This month, Vietnam said it would open its Cam Ranh Bay naval base to foreign warships as a counter to growing Chinese maritime power and threats to its fishing and oil operations in the South China Sea.
Hanoi has accepted Russian aid in upgrading the base - used previously by the US and the former Soviet Union - and is buying Russian submarines and strike jets.
China is also in dispute with Malaysia, Thailand and the Philippines over South China Sea claims, and recently conducted large naval exercises there to underline its determination to enforce its "core sovereignty".
Washington has offered to help mediate, winning approval from South-East Asian countries but angering Beijing, which does not want outside interference and which insists on bilateral, rather than multilateral, negotiations.
But China is also aware that its belligerence could help drive acceptance of America's re-engagement in the region, emphasised by Obama and Clinton during their visits.
To soften territorial chest-thumping, Chinese Prime Minister Wen Jiabao last month announced Beijing would provide the Association of Southeast Asian Nations (Asean) with US$27 billion ($35 billion) in infrastructure and investment funds, and credit facilities totalling US$15 billion.
Further north, tensions continue over the Senkaku Islands in the East China Sea, heightened by the arrest of a Chinese trawler by the Japanese coastguard in the disputed waters.
Japan and China claim the uninhabited islands: China through historical records dating from the 16th century, and Japan through its occupation since 1895, apart from a 27-year spell under US administration after World War II.
Known by China as the Daiouyu Islands, the waters around the chain contain important fishing grounds with large potential reserves of oil and natural gas, driving increasing naval competition between the two countries. Muscle-thumping in the East China Sea is reflecting wider concerns about the growing power and reach of China's Navy, Air Force and strategic nuclear forces.
Hiroyasu Akutsu, of Japan's National Institute for Defence Studies, noted in a paper for Australia's Lowy Institute for International Policy that China is closing the gap in air power held by the US and Japan.
It is also upgrading its strategic strike capabilities, including large numbers of cruise missiles.
Akutsu said this was designed to raise the costs and risks to US forces of operating close to China's coastline or in areas around Taiwan.
At the same time, China protested loudly at exercises by US and South Korean forces in the Yellow Sea, which Beijing insists is within its exclusive military exclusion zone.
But China is becoming more than just an emerging great military power, with its vast economy creating new opportunities and challenges that are testing the skills of policymakers in America, Australia and throughout Asia.
By some estimates, China will eclipse the US as the world's largest economy by 2020.
Its growing influence was recognised formally last month by representation on the governing board of the International Monetary Fund and greater voting power than the United Kingdom, Germany and France.
China accounts for about two-thirds of global iron ore demand, one-third of demand for aluminium ore and more than 45 per cent of demand for coal.
It has vast international investments and is seeking more, especially in agriculture, mineral and energy resources.
Chinese companies have invested heavily in the economies of the Mekong delta and investment by state-owned enterprises in Australia has caused significant political problems.
Increasingly, the trade and economic issues raised by an ascendant China are being woven into national security and foreign policy concerns, potentially fuelling existing tensions.
These became apparent during this month's G20 Summit in Seoul.
Obama failed to win any concessions from Beijing on China's large trade surplus with the US, or on the floating of its currency.
China remains concerned at Washington's renewed interest in the region and its efforts to build a network of free-market democracies.
The US sees this as a balancing act, Beijing as a move towards a new policy of containment.
Noting the need to build a new, inclusive, rules-based regional order, Australian Foreign Minister Kevin Rudd said: "We need to learn from the history of Europe, where the brittleness of international arrangements throughout the 19th and the first half of the 20th centuries gave us wars, and a series of wars."
Giants jostle to influence Asia-Pacific
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