Abraham Fakhuri is a local Lebanese official with a lot of new authority and a lot of new problems. Both have been brought to him by the Israeli Army, now in its eighth week of occupation of this country.

From the balcony of his home on the outskirts of this coastal city, the rotund local agriculture official can point to a field where Palestinian guerrillas fired rockets and cannon at the advancing Israeli Army at the opening of the invasion. The walls of Fakhuri's home are decorated in Lebanese Modern--pockmarks from exploding bullets--and he is glad that the fighting here ended weeks ago and that he and his family are no longer trapped between two heavily armed forces.

Moreover, as a local government official, Fakhuri has already reaped some benefit from the coming of the Israelis. Speaking in Arabic through an Israeli interpreter, he said that when the Palestine Liberation Organization controlled the territory his authority was often ignored. Now, Fakhuri said, the populace is respecting his orders, thanks to the presence of the Israeli Army.

But in the aftermath of the assault, Fakhuri has a whole new set of problems. Like other Lebanese, he is turning for help to the new power in the region--the Israeli Defense Forces. And as those requests multiply, new complications are developing for Israel as it seeks to run a short-term, quiet occupation of a region that has been the undoing of invader after invader.

For one thing, Fakhuri said, disease has spread to the cattle in the area. The Israelis are supplying the necessary vaccine, but it must be refrigerated and as of last week Fakhuri had no electricity. The area was also without running water at the time.

Israeli military officials say they are working as fast as possible to restore such services. Most of southern Lebanon now has electricity, they report.

The essence of the Israeli dilemma is how to provide for what it considers its security needs in southern Lebanon without being drawn deeper into this country's myriad entanglements. One of Israel's announced war aims is the reestablishment of a strong, central Lebanese government, which, it is hoped in Jerusalem, would allow for the withdrawal of Israeli forces and their replacement by the Lebanese Army.

But in a country without a functioning central government since the 1975-76 civil war, that is torn by bitter, longstanding factional disputes, a revival of the art of government will not come easily.

There are already signs of tension. This week the Lebanese government complained at the United Nations that the Israelis are in many cases undermining or ignoring local authorities across the southern region of the country.

Israel apparently sees nothing contradictory in its announced objective of reviving the central government of Lebanon and the presence here of its own substantial Army.

"We have no intention of intervening in internal [Lebanese] affairs," an Israeli official said, adding that "temporarily while the military is in Lebanon we have our security needs."

A local Lebanese official, who said he had no complaints about his town's treatment by the Israelis but who was under no illusions, put it another way. "Israel, once she came, is looking after herself," he said.

Israel will find it difficult now to avoid some involvement in local politics, which tend toward the violent. There has been at least one report of Israeli soldiers having to patrol one town after an unspecified "incident" betweeen local Druze and Christian residents.

Then there is the Palestinian problem, which has shadowed Israel since its birth as an independent state in 1948. Israeli officials have not publicly estimated how many PLO members remain on the loose in southern Lebanon, but there have been reports of as many as 1,000 around Tyre and Sidon.

Sitting in his living room, Ibraham Fakhuri discussed the impact of this. He said his work is being hampered because many of the people under his supervision have refused to return for fear of being picked up by the Israelis as PLO suspects.

Fakhuri's 22-year-old son, Salan, said he was held for 21 days early in the war.

Israeli determination to root out the PLO from southern Lebanon is bound to exacerbate relations with the local populace. One of the methods the Israelis use is to employ local "spotters" who point out suspects. But in an acknowledgement that the method is far from precise, one Israeli official said that the spotters have been known to use their power to settle old scores.

Moreover, Israel has inherited the task of policing the battered Palestinian refugee camps that remain in southern Lebanon even if most of the PLO fighters have fled. Israel has been doing the same thing since 1967 in the occupied West Bank and Gaza Strip, an unpleasant and dangerous business that has tarnished Israel's image in the world.

One day last week on a narrow, dusty street in the refugee camp of Rashydyh, a solid block of people moved toward the Israeli troops guarding the camp entrance. There were about 100 of them, mostly women and children, with a few boys hanging back in the rear.

Gesturing wildly with their hands, they shouted protests at the soldiers. Occasionally one of the women bolted from the crowd, rushing to the guards to scream her complaint. The Israelis ordered them back, at times firing their rifles over the crowd to reinforce the point.

The protest was sparked by the detention of two men the women insisted were innocent of any involvement with the PLO, according to an Israeli official.

"You will see the same kind of thing on the West Bank," he remarked, in a tacit acknowledgement that such sights have become routine in the eyes of the Israelis.

What is to become of the people who inhabit the refugee camps in southern Lebanon has not been settled by Israel's military victory. The Israelis have always considered the camps to be breeding grounds for the PLO and want them dismantled. But the people of the camps, perhaps even more than the PLO fighters in West Beirut, have nowhere else to go.

With the Israeli Army making contingency plans to remain in Lebanon through the coming winter, thought is also being given to the needs of the refugees. There is widespread support in many quarters for dispersing them among the Lebanese populace, in the hope that they would be eventually assimilated.

But, as the independent newspaper Haaretz noted in a recent editorial, this would ignore the wishes of the Lebanese people, for whom the Israelis say they wish only to see a restoration of independence and sovereignty.

How long Israeli troops will be here, guarding the camps, patrolling the cities and towns, is very uncertain. But the longer the Israeli presence in Lebanon continues the more likely it is that Lebanese happiness at the ejection of the PLO will be replaced by other feelings.

If the Israelis do not leave soon, as they have pledged, and their presence stretches through the coming winter and perhaps beyond, "we would consider them an occupation army," said Mouin Jaber, the mayor of Nabatiyah.