Beirut — Lebanon's latest cease-fire is facing pressure from the rivalry between two key outside powers - the United States and Syria. A third key player in the tangled Lebanese equation, Israel, has also been serving notice of its ability to influence events. The most recent demonstration has been Israel's shelling of Tripoli, the north Lebanese port city where Palestinian leader Yasser Arafat and some 4,000 supporters are due for evacuation Monday or Tuesday.
The assumption of commentators, analysts, and newspaper editors interviewed here is that Syria and the US would like to avoid a head-on clash over Lebanon. It is also assumed unlikely Israel will go so far as to attack Arafat's convoy once it actually leaves, with a French naval escort, although the Israelis Sunday were deliberately vague on that point, according to reports from Jerusalem.
The cease-fire between the Lebanese government and the Syrian-backed internal opposition, negotiated in Damascus and announced Friday, is seen as one sign of Syria's recent restraint.
The Americans, for their part, have retreated from using mammoth 16-inch naval guns against Syrian antiaircraft positions in Lebanon. Each shell from these guns, which were fired midway through last week for the first time since the US military came to Beirut some 15 months ago, weighs about a ton and can flatten an area bigger than two football fields. US shelling, which resumed Sunday, involved the US fleet's far less destructive 5-inch cannon.
But the concern among Arab analysts here is that the US-Syrian rivalry over Lebanon may be assuming a momentum of its own, and that long-term US and Syrian interests in Lebanon are, at the very least, starkly different.
On balance, this weekend has been one of Beirut's happier in some time.
The roar of Boeing jetliners over residential areas - anathema to Western environmentalists - resumed Friday to rave reviews here. Beirut airport, shut for 17 days by the latest round of Lebanese violence, was open again as part of the ''permanent and serious'' cease-fire announced in Damascus.
On Sunday, follow-up talks were held there - among the Lebanese, Syrian, and Saudi Arabian foreign ministers - on resuming the Lebanon ''national reconciliation'' talks that recessed six weeks ago. Barring major blow-ups, the conference is expected to reconvene in Switzerland in January.
The next round of talks must still tackle the Herculean task of reconciling internal political, religious, and economic divisions as well as powerful outside interests. Still, Lebanese President Amin Gemayel may at least enter Round 2 with the formal recognition of all parties in the equation.
The Syrian-backed opposition, the Syrians, Libya, and even the occupying Israelis have said in recent weeks they'll deal with Mr. Gemayel as the legitimate voice of Beirut. This process of recognition began on the eve of the first round of reconciliation talks in late October and has continued since then with widened diplomatic contacts by the Gemayel government. This weekend, Mr. Gemayel even visited Libya, a state with which he formally froze diplomatic relations this fall.
But after a lull of several days coinciding with Lebanon's internal cease-fire, US forces in the multinational peacekeeping contingent here Sunday did swap fire with some of the 40,000 Syrian troops in Lebanon.
As in other recent instances, US gunboats off Lebanon's Mediterranean coast opened fire on Syrian-held territory in the inland hills after alleged antiaircraft fire on American reconnaissance flights.
President Reagan has vowed to continue the flights. The Syrians have vowed to keep firing. Indeed, one government-controlled newspaper in Damascus even implied Saturday that Syria would fire on the US boats if the tug-of-war continued.
The fact that the cease-fire talks - and the reconciliation planning - took place in the capital of neighboring Syria was a reminder of how Gemayel's problems are inextricably linked with the interests of other regional and superpower actors.
At issue mostly is a triangle of power and interests involving Israel, which invaded Lebanon last year, the US, and Syria. Each country has military forces in or near Lebanon surpassing those of the central government.
That the cease-fire took hold at all suggests Syria is leery of a major confrontation. Arab analysts here see two main possible explanations for this.
The first is that Damascus has been jolted, at least briefly, by the Reagan administration's suddenly tougher military stance in Lebanon and by the closer US-Israeli cooperation announced after a recent visit to Washington by Israeli Premier Yitzhak Shamir.
The second is that Syrian President Hafez Assad, who has ruled in Damascus for 13 years after an earlier period of frantic coups and countercoups, is more seriously ill than is officially acknowledged. Syrian officials have repeatedly denied this. Syria's prime minister, Abdel Halim Khaddam, was quoted as saying over the weekend that Mr. Assad's health is ''perfect.''
Israel has mostly contented itself this week with issuing public reminders of its ability to tilt conditions one way or the other. In the pine and olive hills southeast of Beirut, the Israeli Army rolled in armor and troops to oversee the end of the siege of Christian militiamen and civilians in Deir al Qamar by Druze forces. This goal had eluded Gemayel's government.
Meanwhile, in Tripoli, intermittent gunfire from offshore Israeli boats served notice they could complicate the planned departure of Palestine Liberation Organization leader Arafat and his Al-Fatah fighters.
The Israeli fire has caused almost no known damage or casualties. But it has made its political point. This was particularly true late Sunday when, as preparations for the Arafat evacuation progressed, the Israelis suddenly opened fire not far from the Tripoli port area.