When the first sniper's round came zinging toward the bullet-pocked apartment building on what residents have come to refer to as the "killing street," Mohammed Ezbeeb yelled from his balcony to warn a neighbor. The second bullet got Ezbeeb in the neck.

The killing of Ezbeeb, 18, on Sunday afternoon was only the beginning of this week's snipings in Shiyah, a Shiite Moslem slum on the southeastern edge of Beirut.

Later in the day, the wife of a Lebanese Army soldier died when a bullet flew into her apartment and struck her in the abdomen. Yesterday, a taxi driver and his passenger were fatally wounded when they drove onto a boulevard in Shiyah and into a hail of bullets.

"This fighting is a habit now, daily," said one of Shiyah's young militiamen as he guided two reporters through a labyrinth of well-trodden alleyways and paths between tenements.

There was more gunfire today and two persons were wounded.

Shiyah faces a Maronite Catholic community along Beirut's old Green Line separating predominantly Moslem and Christian areas.

Snipings and street fighting were common there during the 1975-76 civil war, again in 1978, 1981, 1982, and they are heating up again now.

"Nothing's different," said a shopkeeper on the block where Ezbeeb lived and died, "nothing."

While attention here is concentrated on the war in the mountains, where Druze forces today sprayed Lebanese Army defenses at Suq al Gharb with artillery and rocket fire, Lebanese Army and U.S. military officials are worried about the worsening situation in Shiyah and the other densely populated Shiite slums, which stretch from the edge of the capital to U.S. Marine perimeter positions farther south around Beirut International Airport.

The fear is that the fighting in the mountains overlooking Beirut could merge with an explosion in the slums. Lebanese officials say they are not confident their thinly stretched Army could quell such an uprising. The marines would likely be caught in the middle.

It is far less clear what anybody here is doing to avoid a conflagration.

A Lebanese Army source said today that he has chased Christian Phalangist militiamen from Ain Rummaneh, the community facing Shiyah, but he feared they would return.

A cordon of Lebanese Army soldiers separates the two communities and soldiers arc around Shiyah to seal it and the other Shiite slums from the mountain battles. But the Army's cordon is being tested increasingly these hot summer nights.

The young militiamen say Army soldiers are helping their Christian Phalangist foes and they complain that the guns of the Army cordon are pointed only at them. Sunday night gunmen in Shiyah exchanged fire with the Army units.

Farther south other Shiite militiamen hurled grenades at Army patrols on the road leading to the mountains. U.S. marines who are positioned on the fringes of the southern slums clashed sporadically Sunday evening and early Monday morning with gunmen firing into their positions. The marines returned the fire. There were no casualties.

There are about 8,000 to 9,000 armed men, a large proportion of them teen-agers, in the southern Moslem communities.

When the Lebanese Army moved against militias in western Beirut two weeks ago, they avoided making an all-out effort to remove weapons from the areas on the oustskirts of the city. As a result, militiamen operate more openly in their slum communities than before--although the cordon prevents them from appearing armed elsewhere.

Along the Green Line in Shiyah gunmen operate from a knowledge acquired during eight years of war. There are fixed routes of escape, fixed observation posts and gun positions and seasoned awareness of the way the other side operates.

When the shooting started in Shiyah yesterday, two reporters were in one of the observation posts, a bathroom in a bombed-out apartment with a tiny window that afforded views from several angles of both Christian Phalangist and Lebanese Army positions.

At the first crack of gunfire, a young militiaman in a T-shirt and cutoff jeans, rifle at the ready, jumped into combat position in the garden below.

The elderly of Shiyah huddled in doorways. Small children were herded to safe areas between buildings of thick concrete where they continued their games. As bullets and rockets fell, a toddler in a red dress wandered among them, sucking the last milk from her bottle.

Nabih Berri, leader of the Shiites' political and militia organization, Amal, ordered his militamen today not to fire at the Lebanese Army or into Ain Rummaneh.

Berri said his interest is in achieving political compromises to bring the Shiites, Lebanon's poorest and most populous group, into the mainstream of national life.

But even his confidants wonder how long he can hold the armed young men at bay as the efforts to get a cease-fire in the mountains and begin negotiations to end Lebanon's civil troubles drag on.