One evening this summer, as the sun sank over the vast marble tombs and wrought-iron spires of the Recoleta Cemetery, Argentina's faithful came by the thousands to pray once again for Eva Peron.

Crushed by a disastrous war, the country was beginning another attempt to create the stable democratic government that has eluded it for 50 years. And at the glinting black sepulcher of "Evita," the faithful meant to show that Peronism, the movement she created with Juan Domingo Peron, could still unite and save Argentina.

Then the fights broke out.

There was shoving between the women chanting "Ev-i-ta" and those countering with "Is-a-bel," the name of Juan Peron's last wife and Argentina's last civilian president. There were the burly union men elbowing through to vilify the "traitors" to the cause. Finally, the Peronist youth, marching with broad banners and shouting militant slogans, closed the failed rally down.

That night, the leadership says, has been forgotten, but the sight of the Peronists scuffling around a tomb remains an ominous sign of what Argentina's new transition to democracy may bring. This sprawling, ill-defined movement remains the country's strongest political force outside the ruling military, and its pendulum-like shifts of fortune have shaped the cycle of elections and coups that have plagued Argentina since World War II.

Stripped of its organization by the death of Juan Peron and six years of harsh military rule, the Peronist movement now stands divided into more than half a dozen different factions, ranging from a socialist left to a near-fascist right. It has almost no tradition of internal democracy, and a history of spawning terrorist movements of both ideological extremes.

"It is a situation that can only be understood here," said Jorge Daniel Paladino, a former general secretary of the party. "When Peron lived, we had a movement of people of very different ideas. Now Peron is dead, there has been a freeze (of political activity) of six years, and we have a tremendous confusion."

The course of that confusion is likely to determine whether Argentina fulfills its military government's plans of an orderly transfer of power to civilians by March 1984. If the Peronists are able to rebuild their party peacefully without Peron, they could go on representing working and middle-class Argentines that were largely disenfranchised until Peron rose to power championing their cause in the 1940s.

A collapse of the party, though, could splinter its members into a variety of unstable movements and encourage the partisan feuding and violence that overwhelmed the last Peronist government and led to the military coup of 1976.

In another Latin American country, where political movements built around the leadership and charisma of one strongman have come and gone, Peronism might be expected to melt away into more traditional parties with the death of its leader.

But even eight years after Juan Peron's death and the chaotic failure of the last Peronist government under his widow Isabel, Peronism retains a powerful hold on many Argentines who never knew the principal Peronist era between 1946 and 1955. The nation's union leadership remains overwhelmingly Peronist, and the Peronist youth were invariably the biggest and loudest pack at rallies during the Falklands conflict with Britain.

"The cohesion of the party is always more emotional than rational," said Juan Labake, a former Peronist congressman and one of the party's factional leaders. "It embodies the idea of a universal nationalist Argentine movement."

In many ways, Peronism seems a distillation of the stereotypical Argentine character. Most commonly, it blends a dose of myth with extravagant plans for national greatness, a touch of xenophobia, an absolutist view of what "every Argentine" wants, and an occasional twisting of reality to fit this national dream.

Peron's long administration left a legacy that confuses both his followers and historians. On one side, Peron and Evita built the country's labor movement into the strongest in Latin America, nationalized foreign holdings and built new industries, and heaped benefits on Argentina's working classes.

But Peron, an admirer of Italian dictator Benito Mussolini, confounded his would-be leftist supporters by ruling both his party and the country much like a fascist dictator. He closed Argentina's largest newspaper, amassed a personal fortune, and jailed and tortured political opponents.

The contradictions and muddled ideology of the resulting political movement emerged in full force when the Peronists returned to power between 1973 and 1976. As the country slowly collapsed toward anarchy, the administration veered from policies backed by the Peronist Montonero guerrilla group on the extreme left to those of Isabel Peron and her astrologer aide Jose Lopez Rega, who organized paramilitary assassination squads, on the right.

Although the subsequent military government crushed most of the Peronist left in the late 1970s, all of the old factions have now reemerged following the lifting of political restrictions last month.

And, as in the past, some of their leaders maintain that Peronism has never failed, that its opponents are foreign-backed saboteurs and that ideological differences within the movement can be attributed to "people who say they are Peronists, but really aren't," as leader Antonio Cafiero put it.

One of the few ideological agreements among all the Peronists factions is on the concept of concertacion, or accord, a forming of a national consensus on all political, economic and foreign policies.

"The accord consists of the values shared by all Argentines," Labake said. "It is not a Peronist doctrine but a natural national doctrine, like taking an independent, third position in foreign policy. If it is not a consensus national doctrine, it should be."

Most Peronist leaders also believe that an aggressive program for turning Argentina into an industrialized nation is part of this national doctrine, along with high benefits for the working classes and labor unions. And many, like Labake, dismiss the notion that there are Argentines who do not believe in these goals.

Party leaders say they expect the differences between the traditional Peronists and the reformers -- along with the wide ideological splits -- to be settled by a process of internal reorganization and elections over the next nine months. But this rosy prospect is clouded by the awkward issue of Isabel Peron. Peron's last wife, a former cabaret dancer now in silent exile in Spain, proved to be weak when she became president upon Juan Peron's death in 1974. Most Peronists publicly assert that she remains the head of the movement, while privately suggesting that she will never again assert political leadership. But one vocal sector of Peronism continues to insist that Isabel Peron should be reinstalled as the party's leader.

Thus, say Peronists, the present confusion. "The state of Peronism is like the state of Argentina," said Paladino. "We are not going to be stable next year. We are only going to be stable after the fifth or sixth straight democratic government, and that is the road that we have to see ahead of us."