Ten months ago, Nicolas Ardito Barletta became Panama's first elected civilian president in 16 years, and set out to cure his debt-ridden country's financial problems through economic austerity. His efforts have caused a severe political backlash that could end in a return to military dictatorship.

Panama could soon become the stage for a Latin American replay of what happened last spring in Sudan when President Jaafar Nimeri was overthrown, in large part because he tried to impose drastic economic reforms urged on him by the United States and such multinational lending institutions as the International Monetary Fund.

If Ardito Barletta suffers a similar fate, the ripple effects are likely to be felt far beyond his tiny Central American country of 2 million people. It could seriously impede what Secretary of State George P. Shultz has hailed as a "strong and impressive trend toward democracy in Latin America."

It also would raise anew questions about the effectiveness of U.S. efforts to pressure finan-cially strapped American allies to pursue austere and free-market policies that require their people to make major sacrifices as a means of working their way out of debt.

Panama, whose canal is so strategically and commercially important to the United States, could become a significant example of how difficult it is to help debt-ridden countries without destabilizing their weak governments in ways that put U.S. interests at risk.

U.S. officials, who support Ardito Barletta's efforts to administer the strong economic medicine prescribed for Panama by the World Bank and the IMF, say they believe that the danger of his being ousted has been exaggerated.

These officials concede that he has made a number of costly political mistakes. But they contend that the Panamanian Defense Forces realize that the economy needs a severe shakeout, and would prefer to let Ardito Barletta do the job rather than assume direct responsibility for a difficult and unpopular task.

These U.S. officials note that Panama, with a foreign debt of $3.7 billion, is finding it increasingly difficult to make the $400 million annual interest payments that gobble up 35 percent of its export earnings.

As a result, they say, Ardito Barletta's only hope of renegotiating the payments was to agree to IMF and World Bank demands for the tax increases, spending cuts and elimination of subsidies that have hurt Panama's vested business interests and worsened the country's already severe unemployment.

But the official U.S. view increasingly is disputed by important political and business figures inside Panama and by many outside observers, including some officials of the U.S. banks holding a large share of Panama's foreign debt. Many say that unless Ardito Barletta finds a way to markedly improve his domestic popularity he is likely to be deposed by the military within the next six months.

Gen. Manuel Antonio Noriega, commander of the defense forces, reinforced this view two weeks ago with a public warning issued in Ardito Barletta's presence. Noreiga literally made Ardito Barletta president when he intervened in the May 1984 election to halt a vote count that appeared to favor the other candidate. The result was to make Ardito Barletta the winner by fewer than 2,000 votes.

At a military ceremony attended by Ardito Barletta on Aug. 12, Noreiga harshly criticized the austerity measures adopted by the president at the insistence of the IMF and charged that Panama's economy is "totally anarchic and out of control." The general added:

"We, the Panamanian people, consider that economic intellectuals should give true solutions and not keep their heads buried in books from Harvard or Chicago."

That was a barely disguised reference to the background and thinking that has made Ardito Barletta a special favorite of U.S. policy makers despite the tainted circumstances of his election.

He is an economist who received his doctorate at the University of Chicago when it was the academic home base of professors George P. Shultz and W. Allen Wallis, now underscretary of state for economic affairs. Before returning home to run for president, Ardito Barletta served six years as a vice president of the World Bank in Washington.

Unlike other Latin American presidents who have had to be pressured into accepting austerity, Ardito Barletta entered office as an enthusiastic partisan of the austerity-minded economics advocated by Shultz and Wallis and their allies at the IMF and World Bank.

As one U.S. banker dealing with Panama put it: "He has been holier than the pope, approaching the job like an economist rather than a politician, and with his single-minded concentration on the debt problem he has almost totally neglected the need to build a base of political support."

There are signs, however, that Ardito Barletta has heeded Noreiga's warning and is moving to ease the discontent swirling around him. In a speech Aug. 17, he defended the necessity of austerity but promised to reconsider his agreements with the multinational institutions and seek an easing of their more stringent requirements.

He also called for a dialogue with business, labor and political leaders to seek a consensus on the country's economic course. In addition, he and Mexican President Miguel de la Madrid have been trying to interest other Latin American leaders in banding together to seek a postponement of interest payments to U.S. banks.

Neither the banks nor the U.S. government has shown much enthusiasm for that idea, and other Latin leaders have given it only perfunctory lip service.

But the massive debt pressures weighing on most Latin American countries have started to cause some reassessments of the conventional wisdom that austerity is the only way to deal with the problem.

Peru's new president, Alan Garcia, has vowed to stop dealing with organizations like the IMF and to cap his country's foreign debt payments at 10 percent of annual export earnings. Cuban President Fidel Castro, seeing the debt crisis as an opportunity to increase his influence in the region, is trying to rally Latin America behind demands for a moratorium on debt payments.

Noreiga, who has conducted a sporadic flirtation with Castro, sent five military officers to the recent debt conference sponsored by Cuba in Havana.

If the Panamanian military decides that the way out of the debt crisis lies not with the austerity preachments of Shultz and the IMF but with the radical defiance advocated by Castro and Peru's Garcia, Ardito Barletta and the conventional approach to indebtedness that he has adopted could be in serious trouble.