Secretary of State George P. Shultz's wooing of Syrian support for the Lebanese-Israeli peace agreement is reminiscent of the advice on courtship offered by Kurt Weill's "September Song." Shultz is playing a waiting game, hoping that in time Syrian President Hafez Assad will come his way.

That is the tactic, despite Syrian resistance that seems calculated to chill the ardor of the most determined suitors.

Each day recently has brought a vitriolic Syrian attack on the agreement as a betrayal of Arab interests. As a deliberate snub, Syria barred a visit by President Reagan's special Mideast envoy, Philip C. Habib, "because he is one of the most hostile American officials to the Arabs and their causes."

Without Syria, the agreement negotiated by Shultz cannot be implemented. Israel will not withdraw its 20,000 troops from Lebanon unless there is a simultaneous pullout of Syria's 40,000 soldiers and Palestine Liberation Organization forces in Lebanon under Syrian protection.

U.S. officials believe there are very persuasive reasons for Syria to cooperate eventually.

Among problems acknowledged by U.S. officials are Syria's perennial contention for leadership of the radical Arab bloc that regards accommodation with Israel as anathema; its interests in Lebanon, which could be threatened by warming Israeli-Lebanese relations, and its increasing reliance on the Soviet Union to rebuild Syrian armed forces. That reliance has made Syria a potential pawn in Soviet efforts to counter U.S. influence in the Mideast.

Most other Arab nations, including Saudi Arabia, which gives Syria substantial financial aid, appear to be leaning toward agreeing that Syria should honor its pledge to withdraw if asked by Lebanon. Improved U.S. ties could ease Assad's dependence on Moscow and, most importantly, removal of foreign forces from Lebanon would greatly lessen the risk of renewed Syrian-Israeli warfare that almost certainly would end in Syrian defeat.

Shultz and other U.S. policy makers are known to feel that these arguments will nudge Syria toward cooperation. But U.S. officials have also warned that it could take three or four months before they can tell whether this optimism is justified. Amid the waiting game, Shultz has devised a low-key strategy aimed at most effective use of the limited leverage that can be brought on Syria.

The strategy initially calls for U.S. reliance on friendly Arab governments to pressure Assad. Shultz personally appealed for such support to leaders of Saudi Arabia, Egypt, Jordan and Iraq, and his efforts are being enlarged upon by Habib and U.S. ambassadors.

U.S. officials predict that the Lebanon agreement will win open or tacit backing from all Arab League members except the PLO and ultra-radicals Libya and South Yemen. Given the fractious political nature of the Arab world, there is a big question about how Syria will be affected by other nations' opinions.

Potentially most influential is Saudi Arabia, which is committed to giving Syria $500 million a year and frequently gives more. Part of that largess stems from the Saudi royal family's fear that it might have to rely on Syrian troops to put down a challenge from fundamentalist Moslems.

For that reason, many Mideast experts are skeptical about how much the Saudis would pressure Assad. However, Shultz, who conferred with Saudi King Fahd two weeks ago, is known to feel that, despite ambivalent Saudi public statements, Fahd will make a strong, behind-the-scenes plea to Damascus to support the agreement.

Shultz also has made clear that the United States would assist, if asked, in negotiations between Syria and Lebanon and open talks to improve long-strained U.S. relations with Damascus. That effort has met with rude rebuff.

Shultz has shaken off the snubs with frequent public references to Syria as "a proud country" and reiterations of his offer of a dialogue. He has gone out of his way to stress that Syria has "legitimate security concerns and interests" in Lebanon that must be addressed in withdrawal talks.

Shultz noted that the security zone planned by the Lebanese and Israelis in southern Lebanon will extend to the Syrian border and create a need for guarantees that Israel will not be afforded special strategic advantages in any conflict with Syria.

In Syria, which once included Lebanon, there is still a strong belief that Syria has an inherent claim to special political, economic and strategic concessions from its weaker neighbor.

Aggravating the situation is that, while the majority of Syrians are Sunni Moslems, Assad and his principal aides are of the Alawite sect. They must continually prove good faith with the Sunnis by catering to the most extreme forms of Syrian nationalism.

Syria has exploited deep Lebanese religious and political divisions by forging close alliances with some Moslem and Christian factions. These Syrian allies are bitter enemies of Lebanese President Amin Gemayel, and the desire to maintain the clout of pro-Syrian factions in Lebanon will inevitably affect any deal between Assad and Gemayel.

Many U.S. officials believe that much Syrian hostility toward the agreement is motivated by desire to intimidate the weak Gemayel government so it will be more prone to offer concessions. As one senior U.S. official put it:

" . . . the Syrians have the spotlight of world attention on them. Everything they do or say creates big headlines speculating about the effects on peace for Lebanon. So they're taking maximum advantage . . . to see that . . . Gemayel knows he's going to have to pay a price to get the Syrians out."

Soviet influence comprises the murkiest area in the U.S. analysis of Syrian intentions. Shultz is known to have told Congress that as many as 6,000 to 7,000 Soviet military personnel are in Syria, and the Soviets, in addition to wholesale replenishment of the Syrian arsenal, are believed to be running Syria's air-defense system.

Although previous Soviet arms sales to Syria were strictly for cash, U.S. analysts noted that the current resupply effort is on a scale far beyond Syria's ability to pay. That has led some Mideast experts to conclude that Assad has mortgaged himself to a degree that the Soviets hold an effective veto over his actions.

While Shultz was visiting, Fahd and Egyptian President Hosni Mubarak are known to have told him that Assad obtained Soviet aid relatively free of strings and is determined to avoid being forced to play Soviet satellite.

Mubarak, in particular, argued that Syria's ultimate attitude will be determined by whether Assad can obtain what he regards as "honorable terms" for a withdrawal and by his perceptions of how Israel will react to a prolonged Syrian presence in Lebanon.

U.S. officials also believe that is likely to be decisive, and plan to continue impressing it on Syria. Shultz has pointed out repeatedly that only through a mutual withdrawal agreement will Syria be rid of Israeli troops who in some places in Lebanon are only a few miles from Damascus.

While the Israelis have agreed to sit tight for the time being, they have made clear that they will not tolerate indefinite exposure of their forces in Lebanon to attacks from Syrian-protected areas.

Eventually, the Israelis will react, possibly with a preemptive strike against the Syrian buildup or more likely by retrenching forces in southern Lebanon and adopting a "hot-pursuit" approach to guerrilla attacks.

"Assad is a proud, tough and ruthless ruler," noted a U.S. official, who declined to be identified. "But he's no fool. He knows that even with Russian help, he'd lose such a war. We think the Soviets know that, too, and while they'll undoubtedly make whatever mischief they can, in the end they'll probably counsel prudence and moderation rather than get sucked into a war on behalf of a client who'll lose.

"In the Middle East, you can't always go on the assumption that logic and reason will prevail," he added. "But it's our hope that once the Syrians shift gears from rhetoric to thinking about the consequences, they'll start coming around to the view that it's in their best interest to find a way of withdrawing."