"In the entire history of our movement," an official of the Palestine Liberation Organization remarked, "it has never been the Israelis who cut us down. It has always been other Arabs."

His comment fit the situation that has suddenly developed in the aftermath of Israel's invasion of southern Lebanon.

The Palestinians emerged from a week of fighting spunky, proud, and counting the political gains that Israel had handed them.

Almost overnight, however, their exhilaration has given way to fear over what appears to be a major new attempt by Syria and Lebanon to curb their activities, limit their operations, and reduce still farther their zone of control.

Israel's military campaign cannot be said to have broken the back of the Palestinian resistance, or to have crushed the Palestinian as a fighting force.

Outnumbered 10 to 1 and hopelessly outgunned, they nevertheless fought for a week, suffered relatively light casualities, and emerged with their fighting units intact and their morale high. While they lost a lot of equipment, they had plenty to lose - and replacements have been flowing in.

Politically, the Palestinians feel they gained because of the Israel action - at least in the short run. By fighting the Israelis as other Arabs sat by, they refurbished their image as Arab heroes.

They also feel that they contributed to the breakdown of the Egyptian peace initiative which they fear as a sellout of their interests.

During the past week, they spoke optimistically of continuing their guerilla war against Israel as they dug in along a narrow belt that runs almost the width of Lebanon on the north bank of the Litani River.

Yet, the fact is that the Palestinians are now pinned into a small area with the Israelis to the south and the Syrians to the north. Their supply routes by sea have been cut, leaving them wholly dependent on Syria.

There is now strong evidence, moreover, that the Syrians are going to take advantage of that position to impose on the Palestinian the kind of restrictions that are beyond the power of the Israelis to impose.

For years Syria and the Palestinians have had a love-hate relationship that has led to wild fluctuations in their dealings. Syria has given the Palestinians political support, weapons and money, but has periodically tried to bring the Palestinian movement under the control of Damascus.

The Palestinians have always resisted that, most notably in the Lebanese war in 1976 when they fought against Syrian troops who entered this country to restore order. Now it appears that another such crisis is developing.

"You know we don't trust the Syrians," a PLO official said. "For us the real test is coming how, Another attempt to bring us down politically."

The first sign came last week when Lebanese President Elias Sarkis, a reticient man who never makes policy statements without consulting Syria, issued his strongest condemnation ever of outsiders' "interference" in Lebanese affairs.

Outsiders is a code word for Palestinians, who are regarded here as troublesome interlopers, and for their Arab allies such as Iraq, who were sending in supplies and men to help them.

Sarkis, who was elected during the war and has struggled since to build a government that could run this country, said Lebanon would use every means available to achieve this. He said that included "the methods made available to Lebanon by its own potential and friendships and the methods placed at its disposal, upon its own request, by noble brethren who have borne and continue to bear a great deal" for this country.

His words were immediately interpreted as a sign that he was going to get new help from the Arab deterrent force, a multi-national military force sent here by the Arab League to halt the civil war. It is theoretically answerable to Sarkis, but it is made up mostly of Syrians and takes its orders from Damascus.

The day after Sarkis spoke, the Arab force, which means Syria, announced that it was cutting off the flow of troops and weapons that had been coming into the country to the Palestinians.

Observers here believe there are several reasons why Syria would want to impose new restrictions on the Palestinians and curb their ability to fight.

One is that the Palestinians were turning for aid to Iraq, Syria's bitter ideological ally, and Iraqi troops were beginning to show up in Lebanon.

Another is that Syrian President Hafez Assad has wanted for some time to pull his troops out of Lebanon but feels he cannot until the Sarkis government is strong enough to run the country and keep the Palestinians under control.In addition, Syria is said to fear that if the Palestinians keep fighting in the south they could drag Syria into a war with Israel that it does not want, or at least give the Israelis an excuse to continue their occupation of the south.

The PLO's chief diplomatic negotiator, Farouk Kaddoumi, has been in Damascus the past few days for talks with Syrian leaders about the future of the PLO-Syrian relationship.