EVERYONE KNOWS that in the Middle East promise turns easily to dust. There is no ignoring, however, that the last few days have seen hints of rare promise in the unique relationship between Israel and Jordan. Formally at war, the two nations, or their leaders, are so familiar with each other's strengths and, especially, weaknesses -- personal as well as national -- they could almost be brothers. How else to explain that Shimon Peres and King Hussein now commend the other's "vision" and solicit appreciation for his difficulties? The two men may have met recently. It would not have been for the first time.

Meanwhile, they watch each other anxiously across the Jordan River. Mr. Peres made reasonably good on his pledges to leave Lebanon and to start fixing the economy, and he is moving on schedule to knock on Jordan's door before his brief time in office expires. The king, aware that the clock is running, is taking advantage of the current alignment of forces in the Arab world to make himself a suitable partner. These developments were in train before Tunis and the Achille Lauro, and have survived these excitements, and have even been helped along by the latments of the PLO.

The deal under consideration goes not to an overall settlement but -- be grateful for small steps -- to a way to start bargaining. King Hussein, holder of an exposed throne in an exposed country, needs international and especially Arab company. Mr. Peres moved toward filling that requirement in a United Nations address whose nuances were instantly and angrily pounced on -- good proof of their seriousness -- by his suspicious coalition mates.

Mr. Peres, a leader of uncertain tenure in a country whose nerves are scraped raw by terrorism, needs assurances that any talks Israel enters will only be with those who "represent peace, not terror." The king has no trouble himself meeting this standard, and he is looking for Palestinians who are, in a current phrase, "not PLO but not not PLO": Palestinians acceptable to Israelis and representative of their own people at the same time.

And where are the Americans? The Reagan administration favors peace but, having been burned in the Middle East, shrinks from the scale of commitment the parties feel is essential to make the new diplomatic enterprise eventually flourish. The standoff on new arms to Jordan, with the administration saying yes and Congress saying not now but maybe later, may offer Washington tactical benefits, but undermines the Jordanian position. There is a chance in the Middle East. The United States should help, not impede, it.