Two tragedies, one old and one new, hang over the Middle East these days in the minds of many moderate Arabs who would like to see the so-called "peace process" make progress.

The old tragedy involves the Palestinians: not the Palestine Liberation Organization and its leader, Yasser Arafat, but the 3 million or so Palestinian people still scattered in ghettos and refugee camps throughout the Middle East and Persian Gulf, whose grim fate may be even more obscured by politics today than it has been for the past two decades.

The newer tragedy involves the prospect -- not yet the certainty -- that a rare period of opportunity for progress, even if only to let the peace process begin without any sure sense of where it will lead, is slipping away.

During a recent three-week reporting trip through Israel, Jordan and Egypt, what came across most starkly was the difference between viewing the Palestinian issue from that region and seeing it from Washington.

What one senses is an enormous gulf between the image and the reality that exists on both sides, to the ultimate detriment of the Palestinian people.

The Palestinians do not seem to know how bad their image is, largely because of Arafat, in the United States and many other countries. "They are bright, articulate, energetic people," said one experienced and exasperated American diplomat in the region. "How the hell did they end up with Yasser Arafat representing them around the world?"

In the United States, the Palestinian issue -- particularly since the Achille Lauro hijacking and other recent episodes -- has become so associated with Arafat, the PLO and the identification most Americans make between those names and terrorism that the fate of the Palestinian people as a whole has become even more obscured and overlooked.

Meanwhile, the Palestinians continue to languish as largely stateless, displaced, unwanted people. They are feared and shunted aside not just by Israel but by most Arab states as well while they produce new generations of frustrated young people with no future, some of whom undoubtedly will be tomorrow's terrorists.

If there is to be something closer to peace in the Middle East than there is today, however, it is the view of moderate Arab leaders such as President Hosni Mubarak of Egypt and King Hussein of Jordan that one way or another, the PLO will have to be dealt with, that separating that organization from the Palestinian question as a whole is too much to ask.

"You in America can't understand, really, what we mean," said Mubarak in an interview. "We mean comprehensive peace. Genuine peace. Not just any kind of solution where we can say we reached a solution but terrorism can continue. That's why I'm telling you the PLO is the sole representative of the Palestinians, whether we like it or not. I would like you in the United States to understand this perfectly well. The PLO are people everywhere. They are in the United States, in Europe, in Algiers, in Egypt, in Israel. They are everywhere. So solving the problem and at the same time trying to ignore the PLO, this will never lead to comprehensive peace."

Mubarak does not advocate inviting Arafat or his top lieutenants personally into initial negotiations. Rather his point is that unless Palestinian representation in any peace process has some PLO-approved links, those representatives would have no chance of bringing together the various factions that already split the movement.

There are moderate Palestinians in the Israeli-occupied West Bank and elsewhere who want peace and eschew violence and would be more acceptable to Washington and Jerusalem as representatives. But they have none of the personal protection, either from the Israelis or the PLO, that the PLO leaders have. They live with the ever-present prospect of being gunned down or stabbed to death by more radical Palestinians, as was a 73-year-old West Bank lawyer, Aziz Shehadeh, earlier this month, if they step out of line.

A broader peace in the Middle East remains difficult to envision. The Israelis remain implacably opposed to dealing with Arafat, and it is hard to see what, if anything, Israel would be prepared to give up in land or authority in any deal with the Palestinians and Jordan.

It is hard to see an end to Palestinian attacks on Israelis, since Arafat appears to control less and less of the violence as individual terrorism grows along with that of other groups not under his control.

Syria remains implacably opposed to both Arafat and Israel and remains a central player in the region whose importance seems, to many Arab officials, to be underestimated constantly by American governments.

Meanwhile, Hussein, while wanting peace with Israel and a solution to the Palestinian issue, is not seen to be as bold a figure as was the late Egyptian president Anwar Sadat, who defied his critics in the Arab world and made a daring and lonely venture for peace with Jerusalem.

Hussein leads a country that is only one-tenth the size of Egypt and not nearly as powerful or influential, and whose population is 60 percent Palestinian. He is, by all accounts, unwilling and unable to move toward an actual peace with Israel without broader Arab and Palestinian support.

Yet it is the action of Sadat that forms part of the pattern that now strikes both moderate Arab and Israeli leaders as forming a potentially rare moment in which the next step can be taken.

In effect, Sadat's action means that Jordan is not alone in the Arab world now as Egypt was in 1979, when it signed the Camp David agreements with Israel.

The pattern also includes the following factors:

*Israeli Prime Minister Shimon Peres has won high marks publicly from both Hussein and Mubarak. Peres is viewed by moderate Arabs as taking positive steps toward getting peace talks started, especially by agreeing to some limited international forum as a prelude to direct talks between Israel and Jordan, and by agreeing to meet with a joint Jordanian-Palestinian delegation. Peres, said one top Jordanian official, "is moving better than the United States is moving" on the peace process.

Peres, however, only has 10 months left in the current "national unity" coalition before his Labor Party is to turn over the leadership to the more conservative Likud Party, under which negotiations are widely viewed as less likely to proceed.

*Israel's security in the north, always a concern in the past when there were heavy PLO concentrations in Lebanon, is now improved since the 1982 invasion.

*The recent U.S.-Soviet summit meeting at Geneva, which in one sense indicated that the Middle East was not near the top of the superpower agenda, is also seen in the region as an event that eased tensions generally and could contribute to a better atmosphere for peace talks.

Linked to this is the possibility of improved Israeli-Soviet relations. Peres, in an interview, made clear that he had toughened his demands for Soviet participation in any international conference on the Middle East to include both restoration of diplomatic relations and significant emigration of Soviet Jews. While there is no evidence that either of these demands will be met, there are signs of improved Israeli relations with some Soviet allies and continued rumors of negotiations about emigration.

* have emerged between Israel and Egypt in settling the border dispute over a tiny strip of land known as Taba. Improved Egyptian-Israeli ties, which have been strained over the 1982 Israeli invasion of Lebanon and the Taba dispute, could reinforce any steps by Hussein toward Israel.President Reagan has the continued ability to influence the peace process, if he chooses to, in what Arab moderates hope will be a positive way. There is no doubt among the Egyptians and Jordanians that only the United States can play the key outside role. There is also no doubt of their disappointment in what they believe is the absence of any imaginative U.S. policy or initiatives.

But here, too, as in the case of Peres, Arab leaders say they feel that time is running out on Reagan, that once the midpoint of his second term passes at the end of next year, Reagan will be a lame duck, less able to push new initiatives should they emerge.

*The new and surprise rapprochement between Hussein and Syrian President Hafez Assad is a potential double-edged sword. No one pretends to know exactly where it will lead. It could mean that Hussein is fed up with trying to moderate Arafat, has lost confidence in Washington and has turned to Syria to buttress its security. But it could also mean an effort to soften Syrian opposition to negotiations with Israel.

It is the confluence of these factors that prompts the moderate leaders to feel that both an important moment is at hand and that "time is slipping away," as Mubarak put it. "That's why we should do something in the very near future so as to keep the peace process going. Otherwise, we are going to lose everything," he added.

Mubarak and others feel that the key step now would be to let some kind of international forum take place and see where it leads -- in effect, to separate peace from the process. The United States has been opposed, along with Israel, feeling that Syria and the Soviets could gain more influence than they merit in such a gathering and exercise a veto.

But Peres has now talked of being agreeable to some vague form of international auspices or support that might be a first step toward direct negotiations with Jordan. Last week in Washington, a senior State Department official spoke more positively than the administration has before about some form of an international conference.

There was, he said, "a better understanding today, in the region and here, about possible ways of putting it together so it would be a successful event."

Peres, in an interview, said, "There are occasions in history when you can meet the double requirement of a procedure that may lead to peace and of a coalition that can follow the procedure. I think both are potentially existent. I should regret it very much if it should be missed."

But, he added, "while there are changes in the policies of the Arab countries, there is unfortunately no change in the quarters of the Palestinian leadership. For the last 37 years since the creation of the state of Israel, I cannot recall a single occasion where the Palestinian leadership discovered a window open even when it was open."