The rivalry of two Arab leaders - one pro-United States, the other decidedly less so - dominated Mideast politics this week. All signs are that the pro-US ruler is losing the contest.
He is King Hussein of Jordan. And it is symptomatic of sagging US stock in the Arab world that even he is bitterly resentful of some aspects of Washington's policy - notably its failure, in the King's eyes, to dent Israeli ''intransigence'' on key negotiating issues. His main Arab rival is President Hafez Assad of Syria.
On Thursday, it was announced in Jordan that King Hussein and Palestinian leader Yasser Arafat had agreed on ''principles'' of future ''political cooperation.'' On the face of it, this could jibe nicely with US hopes for progress toward a general Arab-Israeli settlement, since the King's apparent aim is to secure a Palestinian mandate for negotiated peace.
Also on Thursday, Assad finished two days of talks with Lebanese President Amin Gemayel. Assad was hearing out Gemayel's proposed terms, and timing, for surrender to Syria on the future of his country - less than a year after the Americans had ebulliently predicted a Syrian OK on their blueprint for Lebanon. (Gemayel left Damascus without announcing his expected capitulation to Syrian demands that he scrap his May 17 peace accord with Israel. He said the talks went ''extremely well,'' Reuter reported.)
Technically, the issues of Lebanon and Jordan's latest negotiating move are not connected. This is a point made increasingly of late by a Reagan administration under pressure to explain away its policy setbacks in Lebanon. The American reasoning is that, despite the Lebanese crisis, hope remains for US efforts toward a wider peace arrangement involving Israel and relatively moderate Arab regimes like King Hussein's.
Yet this past week has done little to encourage such hopes, highlighting instead the tangle of forces that could easily doom any wider peace moves.
For one thing, Syria is watching every move Hussein and Arafat make. Damascus is convinced their ultimate aim is a US-mediated peace that will isolate Syria militarily and exclude the issue of Israel's occupation of Syria's Golan Heights.
As Arafat arrived in Jordan last weekend, a government-controlled Syrian newspaper pledged: ''Washington will not achieve in Jordan what it failed to achieve in Lebanon. Syria, which was able to impose the will of the Arab world in Lebanon, will also be able to impose it in Jordan.''
How? The Syrians don't say. One option might be to encourage carefully calibrated tension in Lebanon. This would provide a ready excuse for Israel to shrug off any Jordanian negotiating initiative, something the Israeli government seems hopeful of doing anyway.
A government minister on the extreme right of the Israeli government explained why: ''Clearly, what is at issue (in any Hussein initiative) is that Israel give up Judea, Samaria, and Gaza,'' he said, using biblical terminology for the occupied West Bank of the Jordan River.
''There is no doubt but that, for the sake of a few more votes for President Reagan in the US elections, Israel is being asked to put its head in the noose.''
Hussein also blames Syrian-based terrorists for recent bombings in Amman.
But to thwart any Jordanian ''peace'' bid, Damascus may have to do relatively little beyond the victory over US policy it has already achieved in Lebanon.
Key to any Jordanian peace move is the assumption that the US can prod Israel toward meeting at least minimum Arab demands for Palestinian self-government on the West Bank. As a first step, Hussein still insists the US move on earlier assurances that they will press Israel to freeze Jewish settlement there. Arafat would presumably insist on at least the same before giving Hussein anything resembling a negotiating mandate.
But the battering the US has taken in Lebanon has damaged US credibility. Doubly discouraging for the Jordanians is the fact that 1984 is a US election year. Jordanians assume that President Reagan is unlikely to run the domestic political risks of pressuring Israel this year.
The Israelis no doubt hope this is correct. They are willing to negotiate strictly limited ''autonomy'' in the West Bank and Gaza along the lines of the 1978 Camp David accords. But they oppose the wider self-government implied by more recent US policy statements.
In any event, Hussein's agreement on ''principles'' for cooperation with Arafat's Palestine Liberation Organization reportedly stopped short of sealing any specific negotiating formula. The pace of the Hussein-PLO talks - broken off by a politically stronger Arafat almost a year ago - seems cautious so far.
Palestinian sources suggest Arafat wants to be sure of support from at least his own Al-Fatah faction before even tacitly okaying a Hussein search for peace with Israel.