The old unsteady political order here has begun to crumble and changes making possible a new one have begun, but Israel may not have much more time to achieve its apparent goals of crushing the Palestinian guerrillas, ousting the Syrians and imposing its own peace on this war-battered nation riddled with factions.

Whether the process of political change will be consolidated or quickly reversed depends upon how long the fighting lasts and Israel gains.

In the meantime, although the Syrians have begun to pull out of Beirut, they are still entrenched in the eastern Bekaa Valley and have been pouring in reinforcements. Palestinian guerrillas have taken a pounding, but their political and military leadership is still totally intact.

Signs of an emergent order are everywhere, but as one Lebanese political actor remarked today, "There will be no lasting solution if it is just the Israeli Army replacing the Syrian Army and Prime Minister Menachem Begin replacing President Hafez Assad."

As a result of the Israeli invasion, factions armed or financed by either the Syrians or the Palestinians have been greatly weakened at least temporarily, while the Christians, long suspected of connivance with the Israelis, are feeling stronger than ever.

"My contacts with the chiefs of the pro-Syrian parties here have not been answering their phones lately," remarked one Western diplomat. "I'm not even sure they're even still in Beirut. They may have gone to Damascus."

The leadership of the Maronite Christian militia has lately been ecstatic with the lightning Israeli drive right to the gates of Beirut. Its chief, Bashir Gemayel, has already called for a conference of all Lebanese factions to discuss the future.

"The geopolitics of Lebanon is beginning to change. This could lead to something more than a new status quo like the old one, even to a national settlement," was one Maronite leader's enthusiastic assessment.

The latest sign of the old order's breaking apart under the Israeli military presence was a reported agreement by the leftist National Movement, led by the Druze chieftain Walid Jumblatt, to allow the Lebanese Army to take over some of its military positions in the capital and even in its stronghold, the mountainous Chouf region southeast of Beirut.

In the twisted politics of Lebanon, this signified a clear admission by Jumblatt that his movement had been greatly weakened by its failure to oppose the Israeli invaders and that he might have lost his weight as a major political actor.

The accord was all the more significant as Jumblatt had long opposed the Lebanese Army, charging that it is Christian dominated and an undeclared ally of Gemayel's Christian forces.

From the comments of that faction's leaders, he may be more right than wrong. Officials of Gemayel's party today were pushing the idea of the 20,000-man Lebanese Army filling the vacuum left as many of the Syrian peace-keeping troops fled the center of Beirut.

"Any other solution is against nature and artificial," said one highly placed Maronite official. "I think the Army is going to move."

But the Maronites and other Lebanese groups belonging to the 16 officially recognized communities have repeatedly had their hopes of a new political deal favoring them dashed. The Christian Lebanese forces have kept out of the fighting, trying both to distance themselves from Israel, their unacknowledged donor of $100 million in arms over the years, and to position themselves to reap the benefits of the Israeli invasion.

The Christians would like to reestablish the political order that existed before the 1975-76 civil war, one based on a confessional system that assured them political dominance despite increasing minority with respect to the Moslem population.

Presuming the eclipse of Syrian and Palestinian power in Lebanon, the Lebanese forces are pressing for the expulsion of all foreign forces--Syrians, Israelis and Palestinians.

If this did occur by some miracle today, the Maronites might again dominate politics, but in a de facto alliance with the Shiite Moslem faction Amal, which has been growing in strength monthly. Led by Nadih Berri, it is potentially another big winner from the invasion. It proudly took credit today for knocking out two Israeli armored personnel carriers near Beirut's airport yesterday.

But one side effect of the invasion has been to clear the Palestinians from territory in the south, where the Shiite population, the most numerous in Lebanon, is concentrated. Amal may now vastly expand its influence there, particularly if the Palestinian guerrillas are excluded from a 25-mile wide zone north of Israel as Tel Aviv demands.

"I'm not so sure Amal is unhappy with the turn of events," remarked the Maronite official.

If the Israeli invasion is halted within 24 or 48 hours, the hopes of the Maronites may well be dashed yet again. A cease-fire along the lines that exist today would leave the Syrians and Palestinians in a weakened but not fatally undermined position. Gemayel's Maronite faction could find itself in even a worse situation as the Palestinian guerrillas are pushed northward and ever closer to its stronghold in East Beirut.