When the leaders of the world's two biggest economies meet in Hawaii three months from now, U.S. President Barack Obama will still be able to brag to Chinese President Hu Jintao that the United States has more big companies than any other nation on the planet.

In Fortune magazine's 2011 list of the 500 largest companies, the United States leads with 133, four more than Japan's 68 and China's 61 combined.

But a glance back at the 2005 list would give Hu more of a reason to smile. That year China had just 16 companies in the top 500 and the United States had 176, including at least one, Lehman Brothers, no longer around.

Given China's rapid economic growth and its push for Chinese enterprises to go global, former Deputy Treasury Secretary Robert Kimmitt said it is certain the number of big Chinese companies will continue to rise.

But what American business finds disturbing is that most of the Chinese companies are state-owned, including the three in Fortune's Top Ten -- China Petroleum and Chemical Corp (also known as Sinopec) <600028.SS>, China National Petroleum and State Grid , which says it supplies energy to over 1 billion Chinese consumers.

A new dynamic in the world economy threatens the competitiveness of American companies and workers in world markets and undermines our country's core belief in market-based economy, the U.S. Chamber of Commerce and the Coalition of Services Industries said in a joint report.

No adequate and effective international disciplines now exist to deal with this problem, the groups added, complaining that China and other countries lavish regulatory favors and generous subsidies on their state-owned firms.

For now, that most strongly affects American companies that compete with state-owned enterprises or state-supported enterprises in their home market.

But as SOEs and SSEs grow, they are increasingly competing in third markets abroad and they are beginning to compete in the U.S. market, the U.S. business groups said.

A MULTITUDE OF ADVANTAGES

Vice President Joe Biden is expected to raise U.S. concerns about China's state-owned enterprises during talks this week in Beijing with Chinese Vice President Xi Jinping, China's presumed future leader, and with Hu.

The United States believes China should dismantle a set of financial controls that tend to channel cheaper credit to state-owned enterprises, putting their own private companies and foreign competitors at a disadvantage, U.S. Treasury Under Secretary Lael Brainard told reporters on Monday.

The Obama administration also is pushing in the Organization for Economic Cooperation and Development, a group of 34 rich nations and emerging economies, for a competitive neutrality framework to ensure government-supported companies do not enjoy an unfair advantage over private sector firms.

It is not up to the U.S. to question the wisdom of other nations in establishing state enterprises. But it is very much a U.S. concern if the playing field is not level between them and their American competitors, U.S. Under Secretary of State Robert Hormats said in a recent speech.

He ticked off a multitude of advantages that Chinese and other SOEs have used to grab market share.

Lower taxes, less regulation, protected home markets or privileged access to domestic government procurement markets artificially improve the SOEs economies of scale, lowers their operating costs and increases their sales, enabling them to invest in new technology that increase their competitive advantage at home and abroad, Hormats said.

HOPES PINNED ON TRANSPACIFIC PARTNERSHIP TALKS

U.S. business groups support the OECD effort, even though China is not yet a member of the 50-year-old group.

But they place more emphasis on U.S. free trade talks with eight countries in the Asia Pacific region to forge the Transpacific Partnership pact.

China is not part of those negotiations, but five countries -- Singapore, Malaysia, Peru, Chile and perhaps most importantly Vietnam -- which have a history of major state involvement in their national economy are.

In addition, the White House hopes the partnership will lay the foundation for the long-envisioned Free Trade Area of the Asia Pacific, which both Washington and Beijing support as members of the Asia Pacific Economic Cooperation forum.

The United States is pressing for the broad outline of a Transpacific deal by the APEC summit in November, but still is consulting with business and labor groups to craft proposed rules for state-owned enterprises in the pact.

Kimmitt, the former U.S. Treasury official and now independent chairman of the Deloitte Center for Cross-Border Investment, argued it would benefit China to reorient its state-owned enterprises to avoid possible political backlash in the United States and Europe.

The more state-owned enterprises operate like private companies, the more opportunities they are going to have abroad ... I think the Chinese government and its state-owned enterprises have a self-interest in playing by global rules, in opening China's market and in putting its companies on a path to privatization, Kimmitt said.

He likened the fears about state-owned enterprises to the alarm four years ago over Chinese and other sovereign wealth funds that many suspected were making investments for political rather than purely commercial purposes.

A year-long negotiation led by the International Monetary Fund resulted in the so-called Santiago Principles, a voluntary set of best practices for sovereign wealth funds that has helped dampen concerns in the United States.

New multilateral talks on state-owned enterprises could benefit both sides by establishing rules on how they operate, as well as how they are treated by others, Kimmitt said.

(Reporting by Doug Palmer; editing by Jackie Frank)