Six months after its invasion of Lebanon, Israel officially says it wants to see the restoration of a strong central Lebanese government's authority over all of the country. Yet here in the south, in the one-third of Lebanon they occupy, the Israelis appear to have set about undermining that authority, encouraging the creation of local militia groups dependent on them and creating a multitude of direct trade and other ties between south Lebanon and Israel.

Analysts here already refer only half jokingly to southern Lebanon as Israel's "North Bank," a term coined by the former Labor Party foreign minister Abba Eban.

While the Israeli Army has vastly reduced its military presence here from an estimated 80,000 troops this past summer to fewer than 20,000 now, it has set up prefabricated houses, put up Hebrew signs all over the south and begun to tie the economy and life of fully one-third of this nation's 3 million people into its own.

Israel has opened its borders to all Lebanese, established a de facto "free port" in Haifa for Lebanese merchants and created overnight a new booming market for Israeli exports. In fact, with export sales now averaging about $10 million a month, Israel's trade with Lebanon now far exceeds that with Egypt, although this trade is illegal under Lebanese law.

A trip through southern Lebanon offers an eye opener into Israeli occupation policy. There is no evidence that Israel is seeking to supplant the Lebanese civil administration with its own or establish settlements as it has done in the West Bank. But the Israeli Army is clearly in control, intervenes when and where it wants and deals directly with local leaders, militia chiefs and businessmen.

"They are busy creating facts on the ground," said one Western diplomat in Beirut who regards Defense Minister Ariel Sharon as the key Israeli policy-maker for Lebanon. "He thinks the way to deal with this country is to physically dominate south Lebanon."

Israel has repeatedly said it intends to establish a 25-to-27-mile security zone for its northern border.

Here in Sidon, 25 miles south of Beirut, the Israeli Army still has its headquarters in the offices of the Lebanese governor of south Lebanon, Halim Fayad, and has refused repeated requests to move out. It also has 10 or so "liaison units" in various villages which deal with the local administration and increasingly serve as "consulates," providing visas for Lebanese wanting to go to Israel.

In an interview, Fayad said he "very, very seldom" saw Israeli Army officials and mostly dealt with them by telephone.

"Our main problem is getting them to evacuate our offices," he said. "How can our departments function if they don't have offices and our records?"

He said the Israeli Army had at first tried to take over the running of various government departments, assigning officers to them. But, he added, "We did not allow this."

Fayad claimed the local government was running to a "satisfactory degree" from other rented or temporary offices like his own, located in the Lebanese University administration building. But he then went on to cite various cases of Israeli intervention in local affairs.

These included not allowing repairs on the city's internal telephone system for some time; control of the port and the setting of boat hours for Sidon's 400 fishermen; refusal to allow telephone communications between here and Beirut to be restored until last week and an attempt to repair damaged school buildings in place of the local education department.

Fayad would not comment on the Israeli decision to allow inhabitants of the Ayn Hulwah Palestinian refugee camp on Sidon's outskirts to begin rebuilding their homes, even offering to sell them six models of prefabricated houses in direct violation of stated Lebanese government policy.

Visually, After 6 Months, South Lebanon Becoming Israel.

Visually, the Israeli presence is quite striking in many ways throughout the south. For instance, most of the road and village signs along the main coastal road south of here are now brand new Israeli posts written exclusively in Hebrew. In some villages, gas pumps also have Hebrew writing as well as Arabic or English.

Israeli trucks and civilian as well as military vehicles, clearly marked by their license plates, seem as numerous as Lebanese ones along the coastal road. Big Israeli trucks loaded with Israeli goods, or foreign imports now entering through Haifa, can be seen parked here and there on the roadside south of Sidon, transferring their goods onto Lebanese vehicles.

In some cases, the transfers are done right in downtown Sidon within sight of the serail, the main government building, although trading with Israel is officially illegal.

Starting at the Awali River on the northern outskirts of Sidon, the first of the many Israeli-backed militias, that of the breakaway Army Christian leader, Maj. Saad Haddad, becomes visible, checking cars and papers at the bridge under the watchful eye of Israeli soldiers.

His is one of half a dozen militia groups the Israelis are allowing to operate freely in their occupation zone, all independent of each other and dependent on the Israeli Army for logistical support and arms.

During a two-day trip through the south, I saw, interviewed or heard about the following militia groups: Haddad's "Free Lebanon" forces; the East Beirut-based Lebanese Forces; a Shiite "National Guard" under Karim Khalil in Tyre; a separate Tyre port guard under Ibrahim Farran; a village militia under Haidar Daigh in Juniyah and another under Hussein Nabi in Bra'shit; Shiite militamen of the Amal organization and a Druze national guard in Hasbayya.

According to one long-time resident of the south, the Israelis have tried to create separate militias in 13 or 14 villages but so far succeeded only in Juniyah and Bra'shit.

Even the chief Israeli Army spokesman in Sidon, Lt. Col. Aaron Gonen, admits this is an "abnormal" occupation policy, commenting, "Usually you have a military government and it takes away all the arms."

Asked why the Israeli Army has allowed it, Col. Gonen replied, "We are not stopping any militia from organizing itself. We cannot allow Haddad and the Kataeb Lebanese Forces to have arms and the others not."

"The way we see it is that we don't want to pressure any community," he continued. "Our first priority is to have good relations with all the people of southern Lebanon."

In some cases, the Israeli policy of allowing militia groups to bloom seems to be paying off in new friendships. But in others, notably the Chouf Mountains southeast of the capital, it has clearly backfired and turned into a nightmare of renewed sectarian strife even the Israeli Army cannot control.

One of Israel's new friends is Karim Khalil, 33, whose family was run out of Tyre by Palestinian guerrillas during the 1975-76 civil war here and only came back after the Israeli invasion in June. He commands a "National Guard" of perhaps 100 Shiite militiamen which uses American-made radio communications supplied to him by the Israelis. Press reports say he is also getting arms from Israel.

Khalil, while grateful to the Israelis for restoring his family to power in Tyre, seemed to have no illusions about his relations with the Israeli Army.

"They did what was good for them and we benefited," he said in an interview at his waterfront headquarters. "They didn't do it for my good eyes."

Khalil said the Israeli Army did not interfere in local affairs except "when things become critical. They do not intefere in daily life here unless it is a question of security."

The commander, who spoke in English, discounted the likelihood of the various militias in the south fighting each other "because we are all from the same Shiite sect." But he was clearly worried about radio reports he was receiving Thursday of two truckloads of Lebanese Forces militiamen entering his territory and said nothing of a recent shootout between his men and those of Maj. Haddad in downtown Tyre a week ago.

Asked why he thought the Israelis permitted so many militia groups to operate, Khalil said it was because they wanted to be able to say, "Look, we give even arms and allow them to carry arms. It's not like the West Bank or Gaza."

The militia commander seemed uncertain whether to believe Israeli statements that they plan to withdraw shortly.

"They say they are not going to stay forever," he said, adding, "I'm not sure. It depends. They have their own objectives . . . their own demands."