The U.S. approach to the Arab-Israeli conflict generally divides into two schools of thought. One counsels tentative, arm's-length involvement in the Arab-Israeli conflict on the grounds that the Palestinian issue is too hard; that the so-called moderate Arabs aren't all that serious; that the price is more pressure on Israel for concessions than prudent American politicians care to exert.

The second school has it that neglect historically leads to violence; that the Palestinian grievance generates two-edged terrorism directed not only against Israel (and anybody identified with Israel, including us) but also increasingly against promoters of peace, in Europe as well as in the Arab world. So the United States has no choice but to involve itself actively with a steady, even hand.

The good news in recent weeks is that, after five years of wobbling, the Reagan administration may be finally and firmly enrolled in the second school.

Assistant Secretary of State Richard Murphy's recent meetings with Jordan's King Hussein in London and with Israeli Prime Minister Shimon Peres in The Hague are the most conspicuous evidence that there is more to administration policy than bashing Libya as the focus of all evil. In at least some policy-making circles in the administration, it is increasingly accepted that Libyan-generated terrorism is tightly connected to a resolution of the Palestinian issue. Both require closer collaboration with so-called Arab moderates -- not at Israel's expense, but in Israel's interests.

The reasoning derives from recent frustrations. Effective, unilateral U.S. military measures have been shown to be unlikely to work for lack of clear targets. European allies have been revealed as unreliable partners in any collective effort to exert an economic squeeze on Libya.

So there is more and more talk here of a quiet, collaborative effort to enlist Libya's Arab neighbors in the struggle -- discreetly. They have their own reasons to fear Qaddafi, however reluctant they may be to denounce a beleaguered Arab brother publicly. They are in the best position to operate, in ways that the Americans cannot, to support a significant opposition element within Libya centering on the military. But they require the reinforcement of a general U.S. approach that takes into account their interests across the board. That includes their interests in a balanced effort to resolve the Arab-Israeli conflict.

Therein lies the value of Murphy's recent meetings with Hussein and Peres. They signify to each side the United States' willingness to use its influence on the other in an effort to deal with the core question of Palestinian representation.

Nobody's saying that the core problem posed by the fractured Paestine Liberation Organization and its erratic and unreliable chief, Yasser Arafat, will yield easily to diplomacy. And nobody is underestimating the Middle East's bad habit of falling apart when things seem to be falling into place, as witness the cycle of violence that began with the murder of three Israelis in Cyprus last fall.

The characteristic eye-for-an-eyelash Israeli retaliatory strike that killed some 60 people at PLO headquarters in Tunisia; the hijacking of the Achille Lauro ostensibly in reprisal for the Tunis raid; the airport massacres in Vienna and Rome; the Reagan obsession with Qaddafi -- all this seemed to put the Palestinian problem on the back burner.

But it also brought into sharper focus other forces at work. After almost a decade on the sidelines, the Soviets are expanding their Mediterranean naval presence, shipping SAM- 5 missiles to Qaddafi and reportedly angling for naval-base rights in Libya. They are presentinghemselves as an attractive alternative as an arms supplier for Jordan and other "moderates." They are maneuvering through Syria to promote an international peace conference in which they would hope to play a leading role. That's incentive enough for this administration to try to get things moving in a peace- process framework that would freeze out the Soviets.

Finally, there is the urgency that comes from the Israeli political condition. Under the agreement between the two major parties, Labor and Likud, Prime Minister Peres must hand over power to the Likud's Yitzak Shamir in September for the last two years of the four-year term in which the two parties agree to share power in a government of national unity. Hussein may not be able to make the kinds of concessions that would tempt Peres. But if Peres can't be tempted, nobody on the Israeli political scene can be -- least of all the Likud leadership.

So, once again, the brass ring on this grim merry-go-round looks to be tantalizingly within grasp. Peres knows it. Hussein knows it. Now there is increasing reason to believe that the administration knows it. In a part of the world where bad news is the rule, this constitutes good news.