A fragile truce prevails here and for two days now the sound of gunfire has vanished from the streets of the Lebanese capital.

The four days of intermitten fighting that began last Tuesday between Syrian troops and units of the newly constructed Lebanese army as well as Christian militiamen may have cost [WORD ILLEGIBLE] lives. It was the worst outbreak of fighting since the Syrian army moved into Lebanon to end the civil war 15 months ago.

Both Syria and Lebanon are now trying to find a face-saving formula to end the confrontation.

Syrian Foreign Minister Abdel Halim Khaddam, heavily guarded by a Syrian military contingent, arrived here at the head of a Syrian delegation to meet with Lebanese President Eliah Sarkis Saturday. He returned to Damascus yesterday after agreeing to set up a joint tribunal to deal with security violations.

A joint Syrian-Lebanese military committee was formed Friday to investigate the causes of the outbreak of fighting.

The real causes, however, are to be found in the basic instability of the Lebanese political situation, the resentment which all occupying armies throughout history have engendered and less directly, in the changing alliantes and rivalries in the Middle East since the peace initiative of President Anwar Sadat of Egypt.

In the meantime, the citizens of Beirut, who still bear the psychological scars of the civil war, are trying to pick up some semblance of normality.

In the Christian residential districts, where gunfire swept the streets Friday, shops were opening and people were sweeping up broken galss and trying to remove automobiles that had been shot up.

It was not always easy to tell, in a city that still looks like the ruined face of a smallpox victim, which bullet-sprayed walls and shelled houses were hit last week and which were targets in the civil war.

The fighting began with what should have remained a localized incident between soldiers. The old ochre buildings of the Fayadieh Barracks on the Damascus road house the recruits of the Lebanese army which this country is trying to reconstitute after its disillusion with old army during the civil war. The recruits are a mixture of Christians, Moslems and Druze, while most of the officers are Christians.

They are imbued with a spirit of nationalism and they are told that they are being trained to take over the country's security from the Syrians who make up the bulk of the 30,000-man Arab peacekeeping force.

Security, however, has been deteriorating in recent weeks with an outbreak of bombings in Beirut. The Syrians, in what would now appear to have been an excess of zeal in their efforts to tighten security, put up a checkpoint right outside the Fayadieh barracks. The Lebanese saw this as a slight to their sovereignty.

"Pride triggers just about every shooting incident here," said a veteran correspondent of the civil war, and so it was that push came to shove.

Somebody opened fire. Several Syrians were killed and the enraged recruits captured some Syrian artillery and destroyed some Syrian vehicles.

The Syrians called for reinforcements and more Syrians were killed trying to storm the barracks. Casualties among the Lebaneses were light since they were fighting from defensive positions.

A cease-fire was arranged and talks were to begin on Wednesday. But during the night the Syrians brought up tanks and opened up on the barracks with everything they had. The Lebanese held out.

As one Labanese general said later, the Syrians took too many losses to let the incident go. The affair soon grew into a test of Syrian authority in Lebanon.

It was by no means a religious confrontation. Moslems and Druze among the Lebanese fought against the Syrians. By Wednesday the fighting began to spread into the city's Christian residential quarters, and Christian militiamen became involved.n recent weeks the leader of one Christian faction Camille Chamoun, had softened his stand of no national reconciliation until the Palestinian problem had been solved - which meant, in effect, no national reconciliation. It looked as if President Sarkis was making progress in bringing the Moslem and Christian communities back together again.

Some informed sources here say that die-hard Christian separatists used the incident at the Fayadieh barracks to reopen old sectarian sores in an attempt to secure a separate Christian entity and make it impossible for the Syrians to operate within the Christian enclaves. On the other hand, some members of Chamoun's National Liberal Party say that their neighborhoods were attacked by the Syrians first.

Some Moslems and Christians who live right along the "green line" as the dividing cease-fire line is called, appear to have rushed for their weapons when they heard firing on the assumption that one was being attacked by the other.

Whatever the case, the Syrians soon became involved in fighting Christian militamen, and residential neighborhoods were bombarded. The Syrian army, perhaps the best in the Arab world, is trained to fight in the open. It has never done well in built-up areas. Of the approximately 140 dead, perhaps as many as 100 were Syrian soldiers.

Syrian President Hafez, Assad was furious. He was quoted as telling a Lebanese parliamentary delegation that he wanted the new Lebanese army disbanded. The quote has been denied but it has taken on a life of its own.

A three-man Lebanese delegation rushed to damascus Thursday. It consisted of former President Suleiman Franjieh, Foreign Minister Fuad Butros and Lt. Col. Sami Khatib, who is the nominal head of the Arab peace-keeping force. They were read the riot act. Assad reportedly told them that his Syrians had been keeping the peace and sleeping in the rain and mud while the Lebanese army slept in warm beds.

The irony is that the Syrians, who saved the Christians from defeat by the Palestinians and Lebanese Moslems during the civil war, are now fighting the Christians. Chamoun said, "When the Syrians came to Lebanon it was to enforce law and order but lately they have been acting like an army of occupation." there can be little doubt that the Lebanese are growing sick of the Syrians but few responsible leaders see any alternative to their occupation.

The effect of the Sadat peace initiative, which Syria opposes, has been to drive the Palestinians and the Syrians closer together. In the present fighting, the Palestinians have wisely kept out. But the Christians know that while once the Syrians were willing to have the new Lebanese army keep the peace in the south where Israeli-backed Christians are still fighting the civil war, the Syrians are now not eager to deploy the Lebanese in the south. Nor are the Syrians eager to have the Palestinians leave the south where they confront Israel and their Christian allies.