The United Nations begins the process of electing a new secretary general on Tuesday, in a contest that pits the superpowers against the Third World and may prove to be the institution's most important decision of the year.

So far, there are just two official candidates -- Austria's Kurt Waldheim, who is seeking an unprecedented third five-year term, and Tanzanian Foreign Minister Salim A. Salim, who has the formal endorsement of more than half the 156 members.

But there are at least half a dozen dark horses ready to jump into the race if a deadlock develops, a strong possibility.

Although the political and administrative authority of any secretary general is severely limited by the charter and institutional evolution of the United Nations, there remains the power to build or to erode the usefulness of the institution.

Only the most intractable issues eventually come to the secretary general, such as Afghanistan and Namibia, and on these his ability to act as an intermediary is limited.

Even his administrative authority is circumscribed by fiefdoms of his theoretical subordinates, the chiefs of U.N. specialized agencies and some of his own U.N. department heads, each of whom has an independent power base of support from governments.

But the secretary general can still speak out publicly, demonstrate his effectiveness and innovation as intermediary, catalyst or conscience. And so the selection of a new person for the job is always a watershed for the United Nations, and potentially for the world.

Waldheim has conducted a masterful 10-year balancing act to satisfy the demands of the rival power blocs, but the feeling has grown among Third World diplomats that it is time for one of their own to take the helm of the organization they see as the chief international mechanism for the advancement of their common interests.

Waldheim's innate caution is believed to have earned him the support of both Washington -- although U.S. officials there insist no decision will be made until the last moment -- and Moscow.

"An old shoe fits best," Soviet Ambassador Oleg Troyanovsky has said.

The drama begins when the names of Salim and Waldheim are put to the vote in secret ballots at Tuesday's closed meeting of the 15-nation Security Council.

On the first ballot, each man is expected to win the necessary nine votes -- because council members may vote for more than one candidate. But the expectation is that each initially will be vetoed, without prejudice to contesting anew in subsequent rounds.

The United States is expected to veto Salim. In Washington, some perceive him as an anti-American radical. Salim led the cheers in the U.N. aisles when Peking won the United Nation's China seat in 1971, much to the discomfiture of George Bush, then U.N. ambassador and now vice president.

The Soviets are thought to fear that Salim, an energetic and intelligent diplomat with long U.N. experience, would prove an activist as secretary general, and that he is too close to Peking. But Moscow is expected to let the United States apply the veto, to preserve the Soviets' public record of support for the Third World.

The Chinese, who have always preferred a Third World candidate, have let it be known that they will veto Waldheim at least through rounds in which Salim continues to hold the needed nine votes. It is generally believed by diplomats, however, that Peking will blink before Washington.

Many of Salim's votes -- such as those by France, Ireland and Spain, which are expected to support both candidates on the first ballot -- could erode on succeeding rounds, dropping him below nine and prompting China to withdraw its veto of Waldheim.

That would permit Waldheim to triumph in the council. In the past, such big-power action has been conclusive. The 156-nation General Assembly, which must approve the council nominee, has been no more than a rubber stamp. But this year, Salim has emerged as a group candidate, rather than an individual running on his own merits. He won formal endorsement of the Organization of African Unity in June and of the 83-nation Nonaligned Movement last month.

Not all of that support is solid, however, especially as the ballot is secret. The Latin Americans, for example, "are playing a tactical game," says one Asian ambassador. "They are voicing initial support for Salim, hoping he will be blocked by the American veto so that a candidate from their region can emerge as a compromise choice."

Nevertheless, Algeria and other Salim backers have been lobbying for votes to have the assembly reject a council recommendation of Waldheim's candidacy. And the Latin Americans could join African nations to create such an assembly majority in order to promote the deadlock they seek.

Should such a stalemate arise, either in the council or by an assembly rebellion, the dark horses would emerge. Among them:

Carlos Ortiz de Rozas of Argentina, who was vetoed by the Soviets when he ran 10 years ago, but whose country has since improved relations with the Soviet Union by selling grain to it during the American embargo.

Javier Perez de Cuellar of Peru, a former U.N. undersecretary general, who has good relations with the Soviets and the Americans.

Shridath "Sonny" Ramphal of Guyana, who is the secretary general of the Commonwealth, but has thus far generated little enthusiasm among Latin Americans.

Several Mexicans, including Foreign Minister Jorge Castaneda and President Jose Lopez Portillo.

None of these is expected to emerge on Tuesday, an occasion on which several ballots will be cast to test the strength of the two prime contenders, both of whom spent this week lobbying for support in Cancun, Mexico, among the 22 delegations at the economic summit.

Despite the stiff competition, diplomats who are pressed to lay their money on the nose of one horse tend to put it on Waldheim -- perhaps because of his track record as a man with whom all factions can live in peace.