[TEXT OMITTED FROM SOURCE] east, the United States owes President Hafez Assad of Syria more than a formal thank you for his key role in helping free the American hostages in Beirut.

But if the Reagan administration's record with Syria is any indication, that is as far as Washington will go.

For despite the repeated -- and often disregarded -- advice of two earlier U.S. ambassadors here, the administration has chosen to see Syria in black-and-white terms: not as an essential, if often difficult, force and player in the Middle East but as a Soviet vassal out to thwart U.S. and Israeli policies and to promote terrorism.

If nothing else, Assad's active help in freeing the hostages is yet another in a long series of examples demonstrating that Syria has the power to block -- and unblock -- all major decisions in the region.

Were the U.S. administration now to choose to be more forthcoming, diplomats and analysts here are convinced the changes would be apparent first in Lebanon, which now, as in the past decade, remains Syria's number one priority.

Historians, politicians and diplomats argue heatedly over whether Syria is out to exercise hegemony over its Lebanese neighbor, which many Syrians claim was unjustly torn from the motherland when the French set up a separate colonial administration in Beirut in 1920.

But ever since the fighting began in Beirut in 1975, Syria has felt it could not let the endemic violence there continue unabated without running the risk of that violence spilling over and becoming destabilizing at home.

Although it's not the Syrian style to make wish lists, the government in Damascus clearly would like the United States to persuade Israel to get its Army out of Lebanon once and for all. Concomitantly, that would involve disbanding the Israeli surrogates of the South Lebanon Army and ending its involvement in other aspects of Lebanon's internal affairs.

U.S. compliance would represent a major reversal of administration policy and involve the kind of direct pressure on Israel that the president has studiously avoided.

Even before the hostages were released, official Israeli sources were intimating that Syria had masterminded the hijacking and, in any case, could have ended it much earlier.

In fact, such is Israeli-Syrian enmity that any perceived improvement in ties between Damascus and Washington is virtually certain to draw vigorous opposition from Jerusalem. Similarly, Israel is traditionally most relaxed when Washington is convinced that Syria is the Soviets' cat's-paw in the Middle East rather than an astute manipulator of a superpower for its own purposes, as many Arabs characterize the government in Damascus.

At stake now is a possible change in Washington's appreciation of the situation, which has not been a major concern for Israel in years.

Secretary of State George P. Shultz was so humiliated by Syria's success in thwarting his personally brokered Israel-Lebanon troop withdrawal accord of May 1983, that he publicly washed the administration's hands of Lebanon in March 1984.

His predecessor, Alexander M. Haig Jr., raised Syrian suspicions in April 1981 during a familiarization visit to the Middle East that purposely did not include a Damascus stopover. He made a series of statements supporting the Israeli view that the Syrian military presence in Lebanon, then with Arab League blessing, was a factor of destabilization.

A year later, Haig did so little to stop the Israeli invasion of Lebanon that some Israeli and American critics charged that he actually encouraged what turned out to be Israel's longest and most costly war.

That attitude represented a reversal of earlier U.S. policy. Starting in January 1976, then secretary of state Henry Kissinger, with Israeli concurrence, encouraged Syria to intervene militarily in Lebanon to stop the feared emergence of a radical Moslem-Palestinian state. The following year President Carter met Assad in Vienna.

Syria would like a return to such a policy of "positive neutrality," diplomats and analysts here said. Restraining Israel, it is argued, would help stop the seemingly endless "little wars" among Lebanese communities. And that could help Syria rearrange the Lebanese body politic to better reflect the demographic majority of the Moslems in state institutions still formally dominated by the Christian minority.

With the departure of such one-time major outside influences in Lebanon as the United States, France, Egypt, Iraq and Israel, Syria seemingly would stand a fair chance of succeeding now that the Lebanese at long last show signs of exhaustion.

Analysts argue that the United States -- and the fight against terrorism so dear to President Reagan -- could also benefit.

For the hostage crisis, in this view, has proven to the secular Syrian state that the Americans were right in warning long ago that Damascus was indeed playing with fire in tolerating its Iranian ally's efforts to spread its revolutionary religious fervor to the Shiites of Lebanon.

Days before the pro-Iranian Hezbollah, or fundamentalist "Party of God," was blamed for the 24-hour delay in releasing the hostages, sources here insisted that Syria was preparing a major crackdown on that radical group.

Although Syria encouraged the rivalry between Nabih Berri's more moderate Amal militia and the extremist Hezbollah faction because it helped inflict maximum pain on the withdrawing Israeli troops in south Lebanon, diplomats are convinced that Syria now wants Amal to run the border area. Syria, it is said, has achieved its goal of depriving Israel -- and the United States -- of any advantage from the 1982 invasion.

And privately, Syrians point to the calm on the Golan Heights in Israel since the 1973 Arab-Israeli war as an example of what the future of southern Lebanon might be, were the Americans to cooperate.

More immediately, the Syrian role in the hostage crisis has helped Assad break some of the isolation in the Arab world caused by his controversial backing of Berri's month-long siege of the Palestinian refugee camps in Beirut. That policy not only strained Syria's ties with fellow Arabs, but also with the Kremlin, which once again disapproved of his attempts to destroy Yasser Arafat's Palestine Liberation Organization.

But the specter of terrorism hangs over the U.S.-Syrian relationship. Although often accused by Israel, the United States and other countries of harboring terrorist training camps, the Syrians have adopted an outward attitude of detached calm. As if to cast doubts on such allegations, they volunteer that even Israel admits that few Palestinian terrorist attacks against the Jewish state have been launched from Syrian-controlled territory. That is as much as Syrian officials are willing to say publicly, despite mounting accusations that Syria has given at least tacit support to terrorism in many countries.

If a shift in relations with Washington does come, it would mark a remarkable turnabout from the fall of 1983 when Secretary of Defense Caspar W. Weinberger, irate over the terrorist bombing of the U.S. Marine barracks in Beirut, said those responsible "are basically Iranians with sponsorship and knowledge and authority of the Syrian government."