Syria has emerged from its most recent test in Lebanon proclaiming a new determinition to keep its army there and to impose its vision of stability and order on its unhappy neighbour.

If Syrian President Hafez Assad is having doubts or is wavering in the face of Lebanon's intractability, there is no sign of it in the statements of Syrian leaders or in the analyses of experienced diplomatic observers.

The Syrian know they are in a difficult position, in which the risks of pushing ahead and of backing downseem equally great. But in the words of an official of Assad's staff, "We have no choice but to accept the challenge and fight."

Having failed to crush the Lebanese Christian militias through military action, the Syrians are now trying to isolate them politically as they have military, and to discredit them in the eyes of other Lebanese. The aim is to break their grip on the allegiance of their followers and turn other Lebanese against them, forcing them to submit to the authority of the central goverment that Syria is trying to build out of the ruins of the Lebanese civil war.

"People complain that our retailation was harsh," a well-placed goverment official said, referring to the Syrian shelling of Christian East Beirut two weeks ago. "Well, when we have done it three times, they will understand our message."

Information Minister Ahmed Iskander, the official spokesman of the regime, said in an interview that there is "no doubt that getting rid of the outlaw guerrillas, who are cooperating with the enemies of Lebanon, would be benificial to the Lebanese state.

"Enemies of Lebanon," he meant Isreal, which is providing military support to the Lebanese Christians. It is Isreal's expressed intention to protect the Christians from what they call genocide, and Syria's determination to bring to heel the Christians or any other group in Lebanon that opposes the Syrian policy that raises the potential significanse of this confrontation beyond its intrinsic importance.

Syria was stung by international, and especially Americans, critism of its military tactics in the recent round of fighting. Syrian officials say their heavy shelling of residential quarters of East Beirut was justifiable retaliation after provocations by "outlaw gangs" that represent only themselves.

The Syrians point out, justifiably, that in an earlier round they took on the Lebanese Moslems and the Palestinians, and they say this shows that they struck against enemies of the Lebanese state regardless of their religion, not against Christians as such.

But the shelling was viewed outside Lebanon as an indiscriminate and excessive attack in which civilians were killed. Since Syria is anxious to portray itself as a legitimate and well-intentioned presence on Lebanon, observers here believed a change in tactics, if not objectives, is likely.

Diplomatic sources noted that fresh troops recently moved into the Beirut area by Syria are not artillerymen but commandos, suggesting that in any new clash the Syrians may go after the Christians at close range, rather than shelling their redoubts from the hills overlooking the city.

Now that Lebanese President Elsia Sarkiehas withdrawn his threat of resignation, the Syrians are again insisting that it is he who controls the Syrian dominated Arab League peacekeeping force, which provides the legal legimtimacy for the Syrian presence in Lebanon. Sarkis, they say, must decide when and how to use these troops.

But Syria has said that from the beginning, two years ago, and does not really attempt to hide the fact that since it is Syria's army, it will carry out Syrian policy.

"Any group which is trying to divide Lebanon or side with Isreal will be faced by Syria, strongly," information Minister Iskander said.

Outside the Syrian goverment , there is widespread doubt that the Syrians can achieve their aims without wading further into the quagmire that has tied down many of their best troops for nearly two years. Syria's position is often compared to that of Egypt under Gamal Abdel Nasser, who kept thousands of troops in Yemen in costly and-fruitless involvement in a civil war there two decades ago.

Syria is already paying a high price in military terms for its campaign to end the chos in Lebanon.

Its estimated 30,000 troops in Lebanon include an entire infantry division and several thousands of the so-called Praetorian Guard of President Assad's brother Rifaat, according to military sources.

Since these troops are tied down in Lebanon receiving no training and letting their equipment fall into disrepair, military sources believe, Syria has lost whatever credibility it may have had as a threat to Isreal, which when fully mobilized is superior to Syria even in man power.

Furthermore, specialists here believe the Syrian troops lack the training and the leadership for the kind of house-to-house street fighting they might face if the Christian militias decided to have it out with them in East Belrut.

So Sryia is trying to enlist other Lebanese in its campaigns to break the power of the militias.

Foreign Minister Abdel Halim Khaddam, Information Minister Iskander and the Syrian media are stressing this message: the Lebanese Phalange Party under Pierre Gemayel and the National Liberal Party of Camille Chamoun, and their Israeli-supported militias, represent a minority not just among the Lebanese but among the Maronite Christians.

It is these militias, which put their own interest above the national interest and live ouside the law, who prevent Sarkis from rebuilding the country and oblige Syria to retaliate, the Syrian message says.

Iskander and other Syrians recite long lists of Lebanese Christians who have declared their opposition to the Phalange and to Chamoun, and who they say want to cooperate with Sarkis and the Syrians in establishing a stable government that would serve all the Lebanese people.

The most notable of these is former president suleiman Franjieh. He was allied with Chamoun and Gemayel during the civil war against the Lebanese Moslem left and the Palestinians, but broke with them after the recent murder of his son, Tony, and his family, a crime generally believed to have been committed by Phalangist militiamen.

Tony Franjieh was a close personal friend of Rifaat Assad, so his death had more than political significance for the syrians.

Syrian officials talk openly of members of the Franjieh clan exacting revenge on the Phalangist leaders. "They cannot bury their dead or go into mourning until they have had revenge," Iskander noted. They are Arabs before they are Christian or Moslem."

Syrian papers gave prominent play to an interview with Franjieh's other son, Robert, in which he said, as do the Syrians, that the militias do not represent the Lebanese Maronite Christians, much less any other Lebanese.

Playing one group of Lebanese against others in an attempt to create a solid national government under Sarkis, whose leadership capacity is widely questioned, is a difficult maneuver, and the Syrians, one informed diplomat said, "don't believe for a minute that it will work."

So they are preparing for another round of military pressure to obtain their objectives. These are, Iskander said, preventing the partition of Lebanon, "at whatever sacrifice," keeping the peace, "preserving the Palestinian resistance." and "helping our Lebanese brothers in reconstructing and developing their country."

He did not say how long Syria would go on trying to achieve these aims, but there is general agreement here that the end is nowhere in sight.