Even while the sound of gunfire echoes through Beirut, ties of commerce, trade, and tourism are springing up between Israelis and the Lebanese.
''The Lebanese are easy people to deal with,'' says an Israeli Trade Ministry official. ''They try to derive the most benefit from any situation.''
Israeli exports to Lebanon are small but growing. July figures totaled $4 million with $5 to $6 million expected for August, going mostly to south Lebanon but in part to Beirut.
This compares favorably with exports to Egypt, which Israel has found disappointing; these totaled $15 million for all of 1981. Export trade with Greece, another Mediterranean partner, totaled $55 million for 1981.
No one knows how this trend will develop when the fighting in Beirut is over and normal trade resumes between the Lebanese capital and the south.
But some Israelis hope -- given evidence so far -- that with or without a peace treaty Lebanon will become not only a growing export market, but also a conduit for Israeli exports to the Arab world.
To them, the trade also takes on political significance -- a sign of normalizing relations with another Arab country besides Egypt.
Trade is already being conducted in the office of a large building supplies firm on the main road south of Sidon, the biggest city in south Lebanon. Joel Mann, a red-bearded Israeli from Orlan Ltd., suppliers of Haifa, is taking orders for plate glass and cement.
Plate glass has become a major Israeli export to south Lebanon, where new panes are visible in shops along all main roads, replacing those destroyed during the Israeli invasion.
''We would like to build a major hotel in south Lebanon and arrange package deals to visit Lebanon, Israel, and Egypt,'' says Ibrahim Ghaddar, American-educated son of the firm's founder, chatting with Mr. Mann on the side.
Mann is an old hand in Lebanon. His firm has been trading through Israel's ''good fence,'' the opening to the post-1978 Israeli-backed enclave along south Lebanon's border. That border area received $600,000 in Israeli exports in May, 1982, and $800,000 in June, according to Israeli military sources.
Israel's main export items at present are food, clothes, plastics, and building materials, according to the Ministry of Trade and Industry.
Welcoming a well-publicized two-day visit from 26 Lebanese merchants from Sidon, Tyre, and Rashayeh, who were lavishly received during the first week in August, Trade Minister Gidon Patt called the mission ''the first step toward economic coexistence between Israel and Lebanon.'' He added, ''There is no intention whatsoever to expand the economic territory . . . of Israel.''
How this trade will develop once the war ends is not yet clear. While some tensions have already arisen in south Lebanon between Israelis and Lebanese, so far public attitudes mostly range from warm to tolerant.
This could shift, depending on the length of Israel's stay and future political developments. However, skilled Lebanese businessmen have made an art of placing business above the vagaries of politics.
Some Lebanese merchants, used to duty-free imports via Beirut or southern ports, are complaining that Israeli products are too dear. But the Israelis think they can compete with processed food, plastics, and bulky building materials too expensive to import from Europe. So far there are no Lebanese exports to Israel.
Israel is acutely aware of the massive Arab market beyond the local Lebanese trade.
''Our government doesn't know and isn't involved in where our exports go,'' says David Brodet, economics adviser to the Ministry of Trade and Industry. ''But the Lebanese are very sophisticated merchants,'' he adds. ''It could be to the rest of the Arab world.''
One startling link between Israel and the Arab world has already been established in Sidon. El Al, Israel's national airline, is running a bustling office below Israeli military headquarters in the local Lebanese government building there.
Arab nationals, Lebanese, and foreigners, unable to leave via Beirut's besieged international airport, now crowd around the one-room El Al office decorated with posters of bikini-clad snorkelers at Eilat.
Mike Steinman, a Canadian-born Israeli working at the makeshift ticket desk, says El Al issued 350 tickets during its first two weeks of operation to Lebanese, Egyptians, Palestinians, Saudis, foreigners, and others.
''If a Saudi comes he can go to Tel Aviv,'' Steinman says. ''We give passengers their visa on a separate paper so they won't have problems. Then we bus them to Ben Gurion Airport (Tel Aviv) and send them out the same day if possible. If not they stay over in the Avia Hotel and leave the next day -- for a transit point if they are continuing to the Arab world.''
Lebanese flying home can enter via Tel Aviv airport. Some foreign airlines have protested that such passengers flying El Al are given special treatment.
The Sidon office is busy seven days a week. John Wakim, a naturalized Lebanese-American is trying to get back to Boston after visiting a sick father and getting caught by the war. Salam Abdul Rahman, Fiat manager in west Beirut, is trying to get his family out of the nightmare to his brother in Richmond, Va. He finds El Al a safer route than taking a ship from Christian-held Juniye port just north of Beirut. ''If Beirut airport opens, we will pack up,'' says Steinman.
Meanwhile, Israel has just begun short commercial plane flights between Israeli airports and a newly renovated strip in south Lebanon. Israel is also hoping for a brisk tourist traffic between Israel and Lebanon. Chartered buses bringing visiting Jewish groups up to Lebanon have been in operation for weeks. Twenty Lebanese travel agents were hosted at the end of July by the Israeli Tourist Ministry.
One visitor, Hussein Fakih of Sidon, predicted that up to 1,000 visitors a week would soon be coming from Lebanon.
''Please can you tell me how I can get to Jerusalem,'' one Christian Lebanese from Mieh Mieh near Sidon asked a visitor, reflecting Christian interest in seeing the holy places.
The first tour group of 12 Muslims and one Christian from Beirut, Sidon, Tyre , and Nabatyeh paid $200 to a Sidon travel agent for four days in Jerusalem, Tel Aviv, and Galilee. They were greeted by photographers, champagne, and the minister of tourism at a posh Tel Aviv hotel.
But in a reminder that the war is still going on, an Army announcement that Israelis would soon be able to take guided tours to Lebanon added that during the initial stages Israeli soldiers would accompany the buses.