Despite an unremitting hail of U.S. vetoes in the Security Council, Tanzanian Foreign Minister Salim A. Salim remains hopeful that Washington will reconsider what he calls its "misconception about what I stand for, what I would do and not do," and permit his election as the next U.N. secretary general.

Kurt Waldheim of Austria, the incumbent who is seeking an unprecedented third five-year term, remains equally hopeful that China will quit vetoing him.

The next vote on the nomination for secretary general in the Security Council has been set for Tuesday at the request of U.S. Ambassador Jeane J. Kirkpatrick who was briefly hospitalized last week because of an adverse reaction to a change in thyroid medication.

No other candidates have come forward yet, because Salim retains the endorsement of the group of nonaligned nations, and Waldheim retains backing of the other four veto-bearing permanent council members -- Britain, France, the Soviet Union and the United States.

And so more than two weeks into the election process, after eight inconclusive ballots, the race for the top U.N. job remains at an impasse.

Most diplomats indicate Waldheim holds the edge, on the theory that the U.S. veto of Salim is irrevocable, while China's veto of Waldheim is not. Peking has relented twice before -- after initial vetoes of Waldheim in 1971 and 1976. Waldheim has won more than the required nine-vote majority on each ballot this year, while Salim has fallen below that magic figure on five of the eight ballots, including the last.

Washington has never articulated its reasons for opposing Salim or even publicly admitted that it is vetoing him. The general assumption has been that the Reagan administration feels Salim is too radical, too committed to Third World causes.

Salim outlined his case earlier this month to Kirkpatrick, who promised to relay his message to Washington and said publicly that if he was elected, Salim would in her personal opinion make a fine secretary general. But the following day, the United States again vetoed him.

Initially it was thought China would drop its veto of Waldheim when Salim's total dipped below the required nine votes. Now diplomats speculate that China will maintain its stated intention -- to elect a Third World candidate -- in the hope of maneuvering the Soviets into an embarrassing veto of an eventual compromise candidate offered by the Third World bloc.

Waldheim and his backers have remained aloof as the contest continues, with Salim placed on the defensive. Salim took pains in an interview last week at the Tanzanian U.N. Mission to make the point that Washington could relent, and to state his case for why it should.

The 39-year-old native of Zanzibar, who spent 10 years as Tanzania's U.N. ambassador and also got a master's degree at Columbia University, said that in all his discussions with U.S. officials, "I detect no element of hostility toward my person."

As chairman of the U.N. Decolonization Committee, and as president of both the Security Council and General Assembly, Salim was generally recognized to have conducted himself with impartiality.

"I conducted myself in an objective and fair manner, and would expect to do no less in the office of secretary general, which imposes additional responsibilities -- that one is the instrument of all 156 member governments," he said. "One is not secretary general of all nations minus South Africa, or anyone else."

He refused to criticize Waldheim, for whom "I have a lot of personal respect," except to say that "he has done his duty. After ten years you need change."

"Any secretary general," he added, "has to understand the limits and constraints of office, to get the cooperation of the members. In conflict situations, the secretary general must also endeavor to win the understanding of the parties concerned."

Should the United States state conclusively that it will stick by its veto, there are half a dozen compromise candidates waiting in the wings to take on Waldheim, most of them from Latin America.

Among the hopefuls are Javier Perez de Cuellar of Peru, Foreign Minister Jorge Castaneda of Mexico, Carlos Ortiz de Rosas of Argentina and Shridath Ramphal of Guyana, the secretary general of the Commonwealth.