Despite the recent completion of several major projects, Argentina's controversial nuclear development program has fallen behind the military government's ambitious plans and is threatened by funding shortfalls and technical problems, according to Argentine officials and Western diplomats here.

Argentina, which has had a long and aggressive campaign for self-sufficiency in the production of nuclear fuels, reactors and power plants, has been widely regarded by technical experts as capable of exploding a nuclear device within the next five years.

Following the Falkland Islands war with Britain, military officials also publicly edged toward the endorsement of military use of their nuclear technology by announcing they will study the possibilities of constructing a nuclear-powered submarine.

Recent budget cuts, economic stagnation and evidence of continuing technical problems have led many Argentine scientists and Western diplomats to question, however, whether Argentina could summon the means to amass a nuclear arsenal, even if it actively attempted the project.

It is commonly believed that Argentina could make nuclear arms "within a few years," according to one diplomat here. "The question is whether they will have the political will or the large resources to devote to it," he said.

Perhaps the most significant problem in the Argentine program has been a substantial delay in the construction of a reprocessing plant for plutonium, which is considered potentially crucial to Argentina's prospects of stockpiling nuclear weapons.

Vice Adm. Carlos Castro Madero, the chief of Argentina's nuclear agency, said early this month that the plant, which Argentina is trying to build without help from abroad, is not expected to begin full operation until late 1986 or early 1987, about three years after authorities were once expected to complete it.

Naval sources say Argentina's faltering finances, strained by a $39 billion foreign debt and plummeting reserves, also have ruled out any serious consideration of a nuclear submarine program, despite the official announcement of a study.

Already in recent months, Argentina's nuclear energy agency has been forced to accept a delay of at least a year in the construction of its third nuclear power plant and an accompanying facility to manufacture heavy water, which is used in many nuclear power reactors.

Three other plants once scheduled to be built by the year 2000 will also be pushed backed by as much as a decade or more in a revised development plan, officials and diplomats say.

These setbacks have clouded a year of considerable progress in other areas of Argentina's nuclear program that has brought the country several steps closer to self-sufficiency in technology and success in defying international controls on the spread of nuclear capability.

In April, Argentina opened its first plant for the production of nuclear fuels, and early this month a new testing center for nuclear fuels and reactor parts was inaugurated in the sprawling Ezeiza Center outside Buenos Aires. Later this year, the nation's second nuclear power plant, a 644-megawatt generator built with Canadian technology, is scheduled to open near the interior city of Cordoba.

The progress, which has kept Argentina well in front of other Latin American nations in nuclear development, has come despite opposition of U.S. policy-makers, who have unsuccessfully attempted to force Argentina to accept the Nuclear Nonproliferation Treaty and other international controls.

Earlier this year, Reagan administration officials, including Assistant Secretary of State for Inter-American Affairs Thomas O. Enders, publicly expressed displeasure with Argentina's insistence on reserving the right to develop "peaceful" nuclear explosives.

More recently, however, U.S. officials permitted the export of a sophisticated computer for use in the heavy-water plant under construction by a Swiss firm at the nuclear center of Arroyitos.

For Argentine officials, the decision, which followed strong efforts by the Carter administration to block or impose strict controls on the Swiss export of the plant, represented a small vindication after years of deflecting U.S. pressure with deft political maneuvering and stubborn bargaining with nuclear suppliers.

"There has been improvement" in the U.S. policy, Castro Madero said in a meeting with reporters earlier this month. "There has been less interference in Argentine nuclear development by Washington ."

Most of Argentina's nuclear program in the past 25 years has been aggressively directed toward defying that kind of pressure, which Argentina regards as "technological colonialism" by the nuclear powers against developing countries.

To avoid dependence on enriched uranium in the 1970s, Argentine rejected U.S.-built nuclear power plants and turned to West Germany and Canada, which supplied it with heavy-water reactors using uranium that Argentina can supply itself. Government officials have encouraged the development of nuclear construction and mining companies in Argentina, and they expect the country to build its own plants by the end of the century.

This year, with the United States continuing an embargo on the supply of enriched uranium for Argentina's research reactors, the government quickly turned to the Soviet Union, which agreed to supply Argentina with both the uranium and heavy water.

Meanwhile, Argentina has continued to refuse to ratify the Treaty of Tlatelolco, which bans nuclear weapons in Latin America, despite several promises by the government since 1977 to do so. Castro Madero said Argentina has delayed acceptance of the treaty because it wants to agree first with the International Atomic Energy Agency on safeguards that would be applied to Argentina's program.

This fiercely independent policy is a source of great pride to nationalist Argentine military and political leaders.

The continuing political significance of the program was more than evident in early August, when the National Commission of Atomic Energy opened the German-built, high-pressure-circuit test facility at its Ezeiza compound. Nearly a hundred special guests traveled to the heavily guarded complex to sit on folding chairs inside the facility while technicians demonstrated the new equipment -- a show that consisted solely of a roaring, screeching noise through a series of pumps and pipes.

When it was over, the guests nevertheless stood up and applauded.

"You have to understand the psychology of it," a diplomat observed. "The Argentines think that to be a big power, you have to have nuclear technology. And they want to be one of the biggies."

Although government officials have repeatedly insisted that Argentina is interested only in peaceful nuclear development, many diplomats here believe that the military's ambitions also extend to weapons.

Occasional reports that Argentina already has or is actively working on a nuclear weapon have yet to be confirmed, but some Argentine military officials are known to favor such a move and officers in the past have been specifically trained for possible work on a bomb program, sources here say.

Independent Argentine scientists and diplomatic analysts tend to question, however, whether Argentina's severe economic problems and delays in current projects would soon permit such a program.

"We simply do not have enough money, because it would be enormously expensive for us to do it with the means that we have," said one physicist, who added he did not know the details of Argentina's programs.

The Argentines agree that the test of their development -- both conventional and military -- is likely to arrive in the coming years as Argentina struggles to reorganize its economy and political system and the nuclear agency tries to complete such projects as the reprocessing facility without international help.

"We have to adjust to our new economic situation," said Castro Madero, "without falling into pessimism about what we can achieve. These programs cannot be ended."