How Saudi Arabia is quietly working to bring stability to the Middle East

In all his tortuous negotiations in Beirut, United States envoy Philip C. Habib has had one key Arab helper whose role has passed almost unnoticed -- Saudi Arabia.

The Saudis have played a key behind-the-scenes role in nudging the Palestinians toward a formula for their exit from Beirut that the United States could also accept, according to Arab diplomats and American Arab specialists.

It was the Saudis, too, who at a key stage of the negotiations in July coordinated the positions of other Arab states to produce a near-comprehensive Arab plan to receive the PLO evacuees.

And the Saudis will have a key role in the coming months in the complex diplomatic moves that will determine whether the PLO finally opts for political rather than military means to continue its campaign -- as well as in the efforts to patch up war-shattered Lebanon.

The kingdom's conservative rulers have been motivated in their diplomatic efforts so far both by their commitment to the Palestinian cause, and by continuing pressure from neighboring countries and their own citizenry not to let this commitment slip.

The Saudis have established their importance in the current Middle East crisis without so much as breathing the words ''oil embargo'' or ''economic sanctions.''

This might be because, as one leading Mideast expert has argued, the Saudis do not today enjoy the same powerful position in the world oil market that they occupied back in late 1973, when they cut back oil production in support of the Egyptian-Syrian war effort against Israel.

The conservative kingdom's economic links with the United States are marked by an interdependence that is by no means one-way. But the absence of any open Saudi threats during the present crisis stems less from any objective Saudi weakness than from the Saudis' traditional preference for a low-key approach, Middle East experts note.

Saudi diplomats hate to use the word ''sanctions.'' They prefer to talk about their government giving discreet ''signals'' to the US administration concerning its wishes.

Saudi officials recall that in the six months before the imposition of the 1973 oil cutback they sent a steady flow of what they saw as strong signals to the US administration concerning the Arab-Israeli conflict.

But the US, not used to what many Americans consider the obliqueness of the Saudi approach, apparently did not understand those signals.

This time, the Saudi ''signals'' have been coming through to Washington thick and fast. Days after the Israelis first marched into Lebanon, Saudi Foreign Minister Prince Saud Al Faisal flew to Europe to confer with President Reagan and then Secretary of State Alexander M. Haig Jr.

Then in mid-July, the prince was in Washington, this time traveling with the Syrian foreign minister as part of a coordinated Arab League mission to all five permanent members of the Security Council.

In Washington at the same time, and certainly not accidentally, was senior Palestinian negotiator Khaled Hassan. (At one point in Prince Saud's discussions with President Reagan, the President apparently wanted clarification on some point of the PLO position. Phoning from the White House, Prince Saud was able to check directly with Mr. Hassan, who was staying in a nearby hotel.)

Further strong Saudi ''signals'' to the US came in repeated telephone calls from Saudi King Fahd to President Reagan, especially as the fighting in Beirut intensified in the early days of August.

Both the Egyptians and the Saudis emerged early on in the crisis as key governmental intermediaries between the US and the Palestinians. But their approaches, dictated by their differing internal and external priorities, diverged on whether the PLO's exit from Beirut should be linked directly to a US commitment to solve the wider Palestinian issue.

The Egyptians argued strongly for such linkage. Foreign Minister Kamal Hassan Ali stressed to the Monitor while on a recent visit here that: ''Having the armed Palestinians distributed without offering them a political role would transfer them from carrying out military actions across the borders of Lebanon to being radicals in three or four Arab nations.''

The Saudis, according to all the parties in the negotiations, did not press as hard for such linkage. And their view was apparently shared by the PLO leadership once the latter had become convinced that it would be detrimental to hold out in Beirut for wider political gains.

But the Palestinians have so far emerged from their complex three-or four-way contacts with the US convinced that the Saudis have elicited ''a promise'' from the US that it will address the overall Palestinian question seriously after the Beirut crisis is solved.

The PLO will be holding the Saudis responsible for collecting on that promise. Both the PLO and the Saudis say they will be looking in the coming months for a US commitment to ''Palestinian self-determination.''

The indications are that, until the PLO has obtained such a commitment, it will not forswear its military option in the region completely. Their bets are on the Saudis, rather than anyone else to obtain it for them.

For the Saudis, the unsettling conditions in their other major theater of interest, the Gulf, make it more imperative to reach a durable settlement on the Arab-Israeli front.

There have been some reports of low-key signs of unrest inside the kingdom in recent weeks. These reports, unconfirmed and probably unconfirmable, speak of around 180 Saudi professional people being removed from their positions because they were suspecteed of having links with antigovernment Muslim fundementalists.

These reports appear in no way to threaten to shake the ruling Saud family's grip on power in the kingdom. But they do keep up the pressure on the rulers to continue supporting the Palestinian cause.