It is the equivalent of primary time now, and candidates are flying quietly into New York, Washington, Beijing, Paris, Moscow and London, meeting with foreign ministers and other officials with little or no fanfare, and slipping out of town again, often denying they are running for anything at all. Although most Americans have not yet heard of any of the candidates, the winner will instantly become a major world figure.

The job they are running for is, of course, secretary general of the United Nations; Kofi Annan's term ends 31 December.  Historically, the job rotates by region, and by tradition it is Asia's turn. 

But things are never simple at the United Nations, and other regions and nations are disputing Asia's claim to the next "S-G." 

Eastern Europe, in particular, says that it now constitutes a separate regional grouping that emerged after the Cold War, and two people greatly popular in Washington, former Polish president Aleksander Kwasniewski and Latvian President Vaira Vike-Freiberga, have tossed their hats into the ring. 

But any one of the five permanent members of the Security Council can veto the choice of secretary general (it was this power that President Bill Clinton wisely used in 1996 to block a second term for Boutros Boutros-Ghali), and Russia seems virtually certain to oppose any candidate from what it still regards as its former "space."

The U.S. ambassador to the United Nations has said that the world body should not be bound by the rotation system; let the best man or woman be chosen. 

Nothing wrong with that theory, but, as with our own election system, certain traditions are difficult to discard. 

I seriously doubt that the Asians, having allowed Africa to hold the position for 15 straight years (Boutros-Ghali and two terms for Kofi Annan), and not having had an Asian secretary general for almost 40 years (since U Thant of Burma in the 1960s), will allow the brass ring to pass them by again. 

Especially for China, the next S-G -- who would be the first Asian in the post since Beijing took over the Chinese seat in 1972 -- offers a major opportunity that coincides with their newly assertive diplomacy throughout the world. 

And remember: No one who is not acceptable to both Beijing and Washington can get this job, and the two countries have significantly different views of what the role of the United Nations should be. 

The Americans will presumably want a more assertive, reform-minded and interventionist secretary general than China.

Bear in mind also that at the United Nations, Asia may not be what you think. 

For bureaucratic and historical reasons, the Asian group runs from the shores of the Mediterranean to the far islands of the South Pacific; it includes most of the Arab world and even Turkey, which has, in Kemal Dervis, currently head of the U.N. Development Program, an excellent dark-horse candidate respected by all.

A handful of other names have begun to emerge, but I warn the reader inclined to handicapping: The next S-G may well come from names that have not yet surfaced. 

The possibilities include:

· Surakiart Sathirathai, Thailand's deputy prime minister, has been running openly since last year and has visited dozens of capitals around the world. He has the formal endorsement of the Association of Southeast Asian Nations, a solid base from which to launch a candidacy.

· Ban Ki Moon, South Korea's impressive foreign minister, has excellent relations with both Washington and Beijing. But would China accept a secretary general from a treaty ally of the United States, and a diplomat who is deeply engaged in sensitive six-party talks on North Korea's nuclear programs?

· Jose Ramos-Horta is foreign minister of East Timor -- the newest nation in the world and, until recently, itself a war-torn half-island in the South Pacific administered by the United Nations. Ramos-Horta is a Nobel Peace Prize laureate and is well known internationally, but his country is tiny, with only 800,000 people.

· Jayantha Dhanapala, a respected Sri Lankan, served as U.N. undersecretary general for disarmament and as ambassador to the United States. He has been openly campaigning for over a year, but some question the selection of another U.N. bureaucrat right after Kofi Annan.

Anyway, you get the idea. 

As I said, the next S-G may not be on this list at all. The former prime minister of Singapore, Goh Chok Tong, could, for example, emerge at the very end. 

Another dark horse, Prince Zeid Raed Hussein, the deft and elegant young Jordanian ambassador to the U.N., deserves closer scrutiny. 

My guess is that the final decision will not come until at least the end of September, during the annual convention of foreign leaders at the U.N. General Assembly. 

Then, with a deadline staring them in the face, the leaders of the Big Five and other major powers, including India and Japan, will get down to it. 

It is not coincidence that all U.N. secretaries general since the first (from Norway, but pre-NATO) have come from nonaligned countries (Sweden, Burma, Austria, Peru, Egypt, and Ghana). Big aligned countries tend to cancel each other out.

But the job does matter. 

A weak S-G means a weaker United Nations, and although that may please some die-hard U.N.-haters, the United Nations has been an important part of American foreign policy on many issues since the end of the Cold War. 

Right now, for example, the Security Council is about to become a major focal point for the Iranian nuclear issue. 

The secretary general can play an important role on such issues, and it is in the American interest, more often than not, to have a strong secretary general exerting pressure on reluctant or rogue states. 

The same may not be true of China. 

The drama coming up, especially between Beijing and Washington, will be interesting to follow, and will tell us a lot about both the future of the United Nations and the long-term intentions of China on the world stage.