A SHOOT-OUT around the corner from where I live illustrates the slow return of law and order to this wartorn city.

A Lebanese security officer had come to evict a family of homeless Kurds from an apartment where they had been living as squatters. One of the Kurds pulled a gun on the security officer, hit him on the head with it and began firing wildly in the air to summon his friends as he ran into the street.

Within minutes the entire neighborhood was in the street, and Sudanese soldiers of the Arab peace force stationed on the block were firing their automatic rifles in the air to get help.

In the recent past, neighborhood incidents like this one mushroomed into full-scale battles between opposing factions in the civil war, most of whom had no idea what the original squabble was all about.

This time, however, a squad of red-bereted Lebanese security officers roared up shooting their M-16 rifles in the air to clear the streets. They were followed by an armored car with Syrian soldiers of the Arab peace force, their machine gun scanning the street.

There was no battle. That is the order part of the story.

The law part is more confused. The next day the security officer who had been hit on the head returned to the neighborhood with some of his buddies. They caught the Kurd who had hit him and quietly and methodically gave him a beating.

The family still hasn't been evicted.

AS ANOTHER sign of law and order, the government announced that from now on all traffic rules must be obeyed. That means no more mad dashes against traffic on one-way streets, no more driving down the wrong side of the road to pass stalled cars, and no more U-turns.

Traffic lights started working this week and, miracle of miracles, drivers began obeying them. But driving here is so chaotic that to someone who has been in Beirut only during the lawless war period it is hard to believe that people will suddenly start obeying traffic laws.

One traffic jam occurs every day at a major intersection near what was once the dividing line between Christian-controlled and Moslem-controlled areas of the city. Traffic from four major streets pours into that corner, and no car appears to be willing to give way. As a result, traffic is stalled for blocks as each car fights its way across, threading between other cars trying to get through the same intersection.

All the while, as many as four traffic police will stand by, chatting idly with their friends.

In a way, that intersection is a microcosm of Lebanon's civil war: Everyone going his own way and the authorities refusing to enforce order.

MEANWHILE, the Syrian presence here is re-enforced every day by more signs extolling the virtues of Syria's President Hafez Assad and his troops who make up the bulk of the Arab peace force. Almost every stall in a new bazaar set up around a public garden has a picture of Assad. A banner across the road says, "Assad the Hero of the Lebanese Peace." Another banner says, "All Honest People Support Assad and Sarkis," referring to Lebanon's President Elias Sarkis.

These banners were hung by Syrian troops, who also passed out to merchants the pictures of Assad and small signs saying, "Arab strike force for the security of Lebanon and unity of its territory and people."

THE ANCIENT Roman ruins in Baalbek, in the Bekaa Valley 45 miles east of here, suffered minor damage from fighting after the civil war ended in October.

Syrian soldiers camped in the ruins took a group of Western reporters -- in the guise of tourists -- around Baalbek and showed where a rocket had crumbled about three feet of the beautifully carved frieze along the top of the Temple of Bacchus. The soldier said the rocket had been fired at them in late October by Palestinians.

At the nearby Temple of Jupiter, machine gun bullets had smashed into the marble walls. The bullets did not go deep into the marble, but the pieces of lead and the chips are visible.

All told, though, the 1,600-year-old temples survived the bitter fighting all around them. Syrian soldiers said some of the statues have been locked up for safekeeping.

PEOPLE ARE now going out at night here, another sign that normalcy is returning. Cafes on Hamra, the main shopping street, are crowded in the evening and movie theaters are full for the 9:30 show. No longer can a car speed down Hamra at night without encountering any traffic. It used to be that the few restaurants that were open at night were almost empty. Now the better ones are turning away customers.

THE LEBANESE government, strapped for cash and faced with a $6 billion rebuilding job, decided this week to buy a new Cadillac for Premier Salim Hoss. The car will replace one destroyed during the civil war.

HERE IS a good example of the way things get done in the Middle East:

An American asked the man who takes care of his apartment to go down the block and get a bottle of fresh orange juice. The houseman went down and told the doorman to do it. The doorman sent his son. It should have taken 15 minutes at most to get the juice, but 45 minutes later it still had not appeared.

When it did come, the cost was $1.50. When the American went to get the juice himself the day before, it had cost $2.25.