A handful of Lebanese policemen have returned to the streets of East Beirut, taking positions between the Syrian troops and Christian militias who fought each other there a week ago, as the first step in a fragile agreement aimed at averting further bloodshed.

President Elias Sarkis, after more than a week of wavering in which he gave the country not one clue about what he was up to, is expected to announce soon that he will put off his resignation for a few months to see if order can be maintained and a firm accord reached.

As a result, the threat of an imminent renewal of violence has been lessened and the political crisis that would have been caused by Sarkis' departure has been postponed.

But the prevailing view here is that the respited is only temporary because the latest round of fighting, like all those that preceded it, failed to resolve the intractable issues that have shattered this tormented country.

Five violent years have passed since Moslem Prime Minister Saeb Salam quit in a dispute over control of the Christian-dominated Lebanese army. Tens of thousand have died since. The alliances have formed and been broken. International organizations have stepped in - but there is no sign of an imminent end to the struggle over who is going to control Lebanon and what is to be this country's relationship with Israel and the Palestinians.

Implementation of the disengagement agreement in Christian East Beirut, where Syrian troops of the Arab peacekeeping force and Christian militias battled it out last week, began without any official announcement that an accord had been reached. In the vacuum created by Sarkis' threat to resign, it is still not clear who negotiated it on behalf of the government.

It apparently calls for a gradual thinning out of the Syrian forces and the insertion of Lebanese police officers between the Syrians and the Christian militiamen while talks continue about what happens next.

Whether those talks will suceed is questionable. Syria has committed itself to subduing the Christian militias and must either press on with its campaign against them - risking Israeli intervention - or suffer a severe political embarrassment.

The Christians are defiant, demanding that the Syrians get out of Lebanon, and are reinforcing themselves for house-to-house warefare in East Beirut. Sarkis remains powerless to control either side.

The Lebanese Moslem left and the Palestinians are watching events warily, ready to step in to protect their own interests or score points against the Christians whom they battled during the civil war.

At the same time, in a conflict only partly related to that in Beirut, Palestinian guerrillas in the south are harassing United ations troops sent in after the Israeli invasion in March. And the threat of a new Israeli attack is constantly in the air.

Smaller scale violence is almost constant - revenge murders, assassinations, battles within the rival faction, nonpolitical crime.

Beyond that, Lebanon appears to be more and more a victim of its own political system, a blend of law, religion and tradition that held together for years but, once disrupted, has been unable to right itself.

Lebanese factional bosses, mostly backed by armed men, are maneuvering for position - including rival claimants for leadership among the Christians, a struggle already stained by the blood of many victims.

One reason Sarkisdelayed his resignation, according to well-informed Lebanese and Western sources, was that his prime minister, Salim Hoss, a Sunni Moslem like all his predecessors, refused to step down. That menat Sarkis' departure would have left a Moslem as de facto head of state until the election by parliment of a new president - a violation of the unwritten law that the head of state must always be a Maronite Christian.

One reason the Lebanese army cannot be deployed either in East Beirut or in southern Lebanon is that it is similarly paralyzed. It disintergrated during the civil war, but attempts to rebuild it have been slowed by Moslem-Christian rivalry over the relisioud affiliation of the officer corps.

Sarkis, whose legendary caution and inscrutability are now being perceived as signs of weakness and vacillation, has received a steady stream of visitors from all sides calling on him observers here say, is mostly because nobody could come up with any other candidate.

One of the tragedies of the war was that it failed to give rise to any new leaders, any popular figures who have a national rather than factional or religious appeal. The personalities on view in the current crisis are largely the same men who presided over the devastation of the country in the civil war, and the few possible successors to Sarkis who have been mentioned are traditional Maronite politicians.

Christian leaders like former President Camille Chamoun argue that if foreign forces - namly Syris and the Palestinians - would get out of Lebanon, the Lebanese could settle their own differences peacefully.

The Moslems have replied that that would only leave the Maronites free to reassert their traditional dominance over the country's political and economic life.

In any case, the Palestinians are not leaving because they have nowhere to go, and the Syrians have given no indication that they consider their mission in Lebanon finished.